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This is to certify that the

dissertation entitled

APPLICATION OF THE SYSTEMS APPROACH
TO EPIDEMIOLOGIC AND ECONOMIC ANALYSIS OF DISEASE
IN DYNAMIC POPULATIONS

presented by

Howard Scott Hurd

has been accepted towards fulfillment
of the requirements for

Ph.D. degrcein Lg. Animal Clin. SCI.

111,. m”. (MW,

Major professor

Date 5/18/90

 

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APPLICATION OF THE SYSTEMS APPROACH
TO EPIDEMIOLOGIC AND ECONOMIC ANALYSIS OF DISEASE
IN DYNAMIC POPULATION 8

By‘

Howard Scott Hurd

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Large Animal Clinical Sciences

1990

p...
v I

LO“

ABSTRACT
APPLICATION OF THE SYSTEMS APPROACH
TO EPIDEMIOLOGIC AND ECONOMIC ANALYSIS OF DISEASE
IN DYNAMIC POPULATIONS
By

Howard Scott Hurd

This dissertation is directed towards the development of methodologies in
analytical epidemiology and animal health economics. The system to which these methods
were applied is the National Animal Health Monitoring System, and disease frequency and
cost estimation in Michigan dairy cattle. Stratified random sampling of dairy herds, with
prospective observation of one year was implemented. Methodological issues in the
computation of disease frequencies and their variance were addressed and a standard
method proposed. Issues relating to the estimation Of the costs of disease were discussed,
and shortcomings in the standard NAHMS methods noted.

Simulation modelling in epidemiology was reviewed for the purpose of evaluating
alternative modelling strategies to be implemented in the context of N AHMS. A
comprehensive classification scheme for epidemiologic simulation models was proposed.
A risk assessment analysis was performed using conditional logistic regression. The type
of maternity facilities had a significant effect on the incidence of respiratory disease in
calves. The proportion of on farm labor that was hired had an effect of disease in adult
cows, but not in calves. If calves were born in multianimal maternity facilities their odds
of having respiratory disease were 10.6 time greater (p < .1). Estimates Of the effects of

various risk factors on the occurrence of Clinical Respiratory Disease were to be

incorporated into the simulation models of Chapter 7 and 8.

The properties of a distributed delay for modelling infectious disease epidemics
were compared to a stochastic Reed-Frost model. The distributions were similar and it
was possible to achieve comparable average attack rates. This model is proposed for use
in modelling a variety of infectious and noninfectious diseases. The model was applied,
to Clinical Respiratory disease in dairy cattle. The model was approximately predict the
observed annual incidence density for example herds from the database. Many specifics
about the herds were not available to the model, which decreased its precision. The
simulation model was a useful tool for evaluating the long term economic impact of
disease on the farms gross margin of Dairy Income minus Disease Influenced Variable
costs. Many different scenarios could be evaluated with this model. An 80 cow dairy
averaging 15,000 (6818 kg) pounds of milk per cow per year was Simulated over 5 years
with different levels of respiratory disease and compared to a non disease run. The
average, endemic, level of disease cost $121,720. Moderate increases in disease cost
$125,986 over 5 years. If the case fatality rate was increased to 50% in an epidemic

Situation the discounted cost of disease was $160,442 over a 5 year period.

DEDICATION

To Susan

An excellent wife who can find?
For her worth is far above jewels.
The heart of her husband trusts in her,
and he will have no lack of gain...
Her children rise up and bless her;
her husband also saying
"Many daughters have done nobly,
but you excel them all. "

Proverbs 31:10-11,28-29

iv

ACKNOWLEDGEMENTS

I would like to thank the members of the Large animal department that contributed
to this project in a variety of ways. Thanks to: Dr. E. C. Mather for his patience and
flexibilty, Eileen Salmond and MaryEllen Shea for all their computer and word processing
support, RoseAnn Miller for her excellent programming assistance, and my fellow
graduate students for their comraderie.

Special thanks and accolades go to my major advisor, John B. Kaneene (Fearless
leader), for his enthusiasm, encouragement, trust and technical expertise. Other
members of my committee are to be thanked for their encouragement and input, Stephen
Harsh, Stuart Gage, Brad Thacker, and Tal Holms. One of my biggest regrets is that
there was not time to interact much more with all of these talented individuals.

I have been blessed with a family that has provided indescribable support in every
area. I thank my parents for sacrificing and investing in my education as a youth, and
for teaching me it's value. I thank my in-laws for their support, especially C. D.
VanHouweling D.V.M. for his model as a professional and constant encouragement.

There is not gratitude enough available to fully thank my wife for all her life that
she has poured into mine and into this third college degree that we have earned together.

Mostly, I thank my God and Father of the Lord Jesus Christ. (”Let him who

boasts, boast in the Lord" 11 Corinthians 10:17)

TABLE OF CONTENTS
LIST OF TABLES
LIST OF FIGURES
INTRODUCTION
SYSTEM APPROACH
NEEDS ANALYSIS
PROBLEM STATEMENT
OBJECTIVES
OVERVIEW
CHAPTER 1. The National Animal Health Monitoring System
in Michigan I. Design, data, and frequencies
of selected dairy cattle diseases.
ABSTRACT
INTRODUCTION

MATERIALS AND METHODS

I...

 

vi

10

11

RESULTS
DISCUSSION
CHAPTER 2. The National Animal Health Monitoring System in Michigan 11:

Methodological issues in the estimation Of frequencies of
disease in a prospective study of multiple dynamic populations.

ABSTRACT

INTRODUCTION

METHODS

r 1 ion d llecti n

Eng prgfiuct te be eetimatfi
HEW
Eepuletien estimates efi genual ineidence
nganee estimates ef mung; incidence
Risk estimefien

CONCLUSIONS

CHAPTER 3. The National Animal Health Monitoring System in
Michigan 111. Cost estimates of selected dairy cattle diseases

ABSTRACT

INTRODUCTION

MATERIALS AND METHODS
r n 1 i n 1 n
'm i In 1 ' ' rd

vii

12

16

18

18

20

2O

2O

21

22

24

25

28

30

30

31

32

32

33
33

Was
RESULTS

DISCUSSION

CHAPTER 4. The Application of simulation models and systems analysis

in Epidemiology: A review
ABSTRACT
INTRODUCTION
HISTORY
CLASSIFICATION

Clegsifigtien methgl

ne m elt

6

fr st s'mtin

f

aifi'nfli 1

DISCUSSION

W

CHAPTER 5. Risk factors associated with clinical respiratory disease in Michigan
dairy cattle: Analysis Of data from the National Animal Health

Monitoring System
ABSTRACT
INTRODUCTION

MATERIALS AND METHODS

viii

SI

'm tes

34

34

4O

4O

4O

42

44

44

45

48

49

54

58

62

63

65

65

68

er e1 ' dda 01 tion
Stetisg’ggl grelysis

RESULTS

DISCUSSION

CHAPTER 6. A Stochastic distributed delay model of disease processes in
dynamic Populations

ABSTRACT

INTRODUCTION

MATERIALS AND METHODS

r ' ° t l

Estimetien ef the eutpet distributien
Estimation ef DEL
Epidemie thresheld thmrem appliQ
Intrmuction ef steehestieig

mm
RESULTS
DISCUSSION

CHAPTER 7. Application of a stochastic distributed delay simulation model
to the epidemiology of clinical respiratory disease in a dairy
cattle population.

INTRODUCTION

MATERIALS AND METHODS

W

68
69
7O
77

82

82
82
84
84
88
9O
9 1
92
93
94
100

102

102
102

102

Cempetatienal methgfls
Emmeter estimatieg
Semnm Attack Rete
W

RESULTS
Predieted versus simelated disease frmuencies
WM

DISCUSSION

SUMMARY

CHAPTER 8. Application Of a stochastic distributed delay simulation

model to economic analysis of Clinical Respiratory Disease
in Michigan dairy cattle

INTRODUCTION

MATERIALS AND METHODS
Mgflel Appligtien

RESULTS

DISCUSSION

SUMMARY AND CONCLUSIONS
APPENDIX A
APPENDIX B
APPENDIX C
APPENDIX D

BIBLIOGRAPHY

108

109

111

112

113

113

114

114

116

117

117

118

126

127

127

129

130

136

138

145

176

Table 1.1

Table 1.2

Table 1.3

Table 1.4

Table 3.1

Table 3.2

Table 3.3

Table 3.4

Table 3.5

Table 3.6

LIST OF TABLES

Projected and achieved Michigan sample characteristics Of dairy
herds in round 1.

Most frequently reported disease problems in Cows, expressed as
mean incidence densities (one standard deviation) per 100 cow
years.

Most frequently reported disease problems in Calves, expressed as
mean incidence densities (one standard deviation) per 100 animal
years.

Most frequently reported disease problems in Young Stock,
expressed as mean incidence densities (one standard deviation) per
100 animal years.

Total dollar cost of disease per COW per year (including cost of
prevention).

Total dollar cost of disease per CALF per year (including cost of
prevention).

Total dollar cost of disease per YOUNG STOCK per year
(including cost of prevention).

Annual cost Of preventive measures of the top 10 disease problems
of COWS (expressed as mean U.S. dollars per cow).

Annual cost of preventive measures of the top 8 disease problems
of CALVES (expressed as mean US dollars per calf).

Annual cost of preventive measures of the top 8 disease problems
of YOUNG STOCK (expressed as mean US dollars per animal).

xi

13

14

15

15

35

36

37

38

39

39

Table 4.2

Table 5.1

Table 5 .2

Table 5. 3

Table 5.4

Table 5.5

Table 5.6

Table 6.1

Table 7.1

Table 7.2

Table 8.1

Table 8.2

Table B.1

Classification of applied epidemiologic structural process models

Dichotomization of dependent variable (ID) for use in the
conditional logistic regression, by age group.

Variables tested in general linear model (GLM) for effect on the
annual incidence density of respiratory disease in COWS and
YOUNGSTOCK (number of positive responses, or mean).

Variables tested in general linear model (GLM) for effects on the
annual incidence density of respiratory disease in CALVES(number
of positive responses, or means).

Variables in the final GLM model for respiratory disease in
CALVES. Conditional Odd ratios for interesting variables, adjusted
for herd size strata.

Variables in the final GLM model for respiratory disease in
YOUNG STOCK. Conditional odd ratios for interesting variables,
adjusted for herd size Strata.

Variables in the final GLM model for respiratory disease in COWS.
Odds ratios for interesting variables, adjusted for herd size strata.

Comparison of Reed-Frost and distributed delay stochastic models.

Epidemiologic model parameters. Average daily rates from
Michigan NAHMS Round 1 and literature.

Observed and Simulated annual incidence. densities (aID) for
NAHMS herds. Herd specific sizes and loss rate used for each
model run.

Economic parameters for the ”average" dairy herd

Simulation results for "average" Michigan dairy herd with different
levels of disease, 5 year runs.

Disease groupings used in NAHMS in Michigan in round 1,
1986/87.

xii

59

69

73

75

76

77

94

110

113

119

128

137

Eiam

Figure 2.1

Figure 4.1
Figure 4.2

Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6.

Figure 6.7.

LIST OF FIGURES

Flow chart of various disease frequency measures proposed, with
definition and expected use.

Proposed Classification Method for Process Epidemiologic Models
Genera of Epiderrriologic Process Models

Infectious disease application of the proposed distributed delay
model. NONCX = Nonclinical state, CLINICAL = diseased

Schematic diagram of proposed distributed delay model for
infectious and noninfectious diseases. N ONCX = nonclinical

Family of Erlang distributions for waiting times to exit, which can
be represented with a distributed delay. E[r] = average waiting
time to exit. (Manetsch, 1966)

Triangular distribution assigned to B. The minimum (MIN),
maximum (MAX) and MODE must be defined.

Frequency distributions (100 epidemics) of distributed delay
(DDEL) (a) and Reed-Frost (b) stochastic disease models for p =
.0016 and B=.0016, TRIANGULAR distribution.

Frequency distributions (100 epidemics) of distributed delay
(DDEL) (a) and Reed-Frost (b) stochastic disease models for p =
.0012 and B = .0012, TRIANGULAR distribution.

Frequency distributions (100 epidemics) Of distributed delay
(DDEL) with EXPONENTIAL distribution (a) and Reed-Frost (b)
Stochastic disease models for p = .0012 , B = .0006.

29

50

55

85

87

89

93

96

97

98

Figure 6.8

Figure 7.1a
Figure 7.1b
Figure 7.1c

Figure 7.2

Figure 8.1a

Figure 8.1b
Figure 8.2

Figure 8.3

Frequency distributions (100 epidemics) of distributed delay
(DDEL) with EXPONENTIAL distribution (a) and Reed-Frost (b)
stochastic disease models for p = .0016 , B = .001.

Epidemiologic simulation model of the Animal POpulation and
Production System (APPS) for CALVES.

Epidemiologic simulation model of the Animal Population and
Production System (APPS) for YOUNG STOCK.

Epidemiologic simulation model of the Animal Population and
Production System (APPS) for COWS.

Observed distribution of Secondary Attack Rate in CALVES.

Dairy income and Disease influenced variables cost for CALVES
and YOUNG STOCK. Block diagram

Dairy income and disease influenced variable cost for COWS.
Computation of expenses associated with CLINICAL disease.

Bimodal distribution of number of cases from DISEASES.

xiv

99

104

106

107

114

121

122

123

128

INTRODUCTION

SYSTEMS APPROACH

A variety of definitions might be used to describe the systems approach. For this
student, the definition, represents an amalgamation of input from a variety of different
disciplines, from electrieal engineering, entomology, economics, and epidemiology. The
consistencies in the various definitions are distilled into the following essential features:
1) a methodology for solving unstructured problems 2) that begins with a defined set of
needs, 3) moves to a description of the whole system as it currently exists, 4) generates
alternatives for meeting the expressed needs, 5) evaluates those alternatives with various
modelling techniques, and 6) designs and 7) implements the policies found most capable
of meeting the needs (Checkland, 1981:161-191; Manth and Park, 1982:8-15).
The procedural steps, of the Systems Approach, outlined by Kitching (1983) provide the
outline for this dissertation and the course pursued in completing this work, those steps
are: 1) problem definition, 2) system identification, 3) decisions on model type, 4)
mathematical formulation, 5) decisions on computing methods, 6) programming, 7)
parameter estimation, 8) validation, 9) experimentation. It should be noted that model
building is only a part of the Systems Approach and a computer simulation model is a

byproduct or tool of the effort.

NEEDS ANALYSIS

The National Animal Health Monitoring System (NAHMS) was initiated in order
to address the problem of ”substantial losses" in the United States livestock industry as
a result of endemic disease. and other animal health problems. The USDA's Animal Plant
Health Inspection Service (API-IIS) became the lead agency in a "comprehensive effort to
develop methedelegy for securing_inf_Qunanen on disease prevalence, incidence, and
economic costs" (King, 1983). Michigan was one of the original pilot project states
involved in this methods development effort (Kaneene and Hurd, 1986). The needs of
the NAHMS, as stated by Dr. King, form a basis for a large portion Of the problem
formulation for this dissertation; ”we need new techniques for evaluating the causes,
interactions, and economic consequences of complex disease syndromes on a national
level. "

Specifically, most modern livestock diseases are multifactorial problems, with
multiple risk factors associated with their occurrence. Interaction and synergism is often
suggested between factors, and the effect of a causal factor may change over time.
Current experimental and analytical methods aimed at addressing the above issues have
certain disadvantages. For example, results from experimental and laboratory methods
are not readily generalized and have low external validity, and can only study one or
two risk factors at a time. However, they have the advantage of good control over
extraneous variables. Observational field studies are often expensive and time consuming,
difficult to replicate, and it is impossible to hold all other variables constant while

changing only one. Multivariate statistical models cannot measure the effect of changes

3

in population structure as it relates to disease occurrence, and they assume that causal
interactions should be controlled or transformed away (Koopman, 1987). Most
procedures fit a model by variance relationships versus biologically plausible pathways,
and have difficulty dealing with the effects of time (MacVean, 1986; Altman, 1988).
Simulation models in epidemiology often ignore different levels of structure within a
population, such as age groups, (Bailey, 1975), and are often mathematical modelling
exercises versus byproducts of a problem solving methodology. Models for evaluating
the economics of disease control are usually based on static estimates of disease, or
predetermined costs, and cannot model changes in rates of disease or costs due to changes

in the population structure, ie. feedback (Willadsen, 1977).

PROBLEM STATEMENT

Analytic epidemiological methods need to be developed that can use observations
from field studies of animal populations, particularly the National Animal Health
Monitoring System, to quantitate the relative and economic effect of various risk factors
on the occurrence of multifactorial diseases in dynamic populations and to predict the

effects of disease control strategies over time.

OBJECTIVES
The general Objective of this dissertation is to apply the Systems Approach to the
unstructured problems of multifactorial disease analysis. The specific objectives are 1)

to describe the system in question; including disease frequencies, cost estimates, statistical

4

properties of the frequency measures used, and factors associated with the occurrence of
clinical respiratory disease; 2) to develop a generic epidenriologic simulation model for
the dairy herd that will provide the realism, and flexibility to address the multifactorial
dynamic disease analysis problems; and 3) to quantitatively determine the effects of
changes in the level of various management characteristics on the economics of clinical

respiratory disease syndrome.

OVERVIEW

An overview of the entire work is present here to facilitate cohesiveness. Chapters
1-3 are not focussed on specifically on respiratory disease but present the methodology
relating to sampling and data collection procedures. They should be considered as the
System Identification phase of the project. Chapter 2 was required in order to define the
exact methods to be used for the computation of disease frequencies used throughout the
project. This represents a unique contribution, as this methodology had apparently not
been developed, for prospective monitoring systems with sampling of multiple
populations. Chapter 3 describes the gross, short term costs of common clinical diseases.
This chapter also discusses some of the shortcomings of the economic methods and
suggests ways to improve the cost estimates. Chapter 4 describes the current state of
applied simulation modelling in human and veterinary epidemiology. Chapter 4 is part
of the alternative model evaluation phase of the Systems Approach. Chapters 5-8
represent the modelling phase of the Systems Approach. Chapter 5 is an application of

the ”standard"- epidemiologic statistical (associative) models, the conditional logistic

5

regression, and linear regression with categorical and continuous independent variables,
the intent of this analysis was to provide information as to important variables to be
included in the simulation model of Chapter 7 and 8. Chapter 6 proposes a generic type
of disease process model to be used for infectious and non infectious diseases, and serves
as a form of validation for the main theoretical subunit to be used in the applied model
of Chapters 7 and 8. Chapter 7 applies the model of chapter 6 to Clinical Respiratory
Disease in 3 ages of dairy cattle. Chapter 8 demonstrates the utility of the model, from
Chapter 7, for improving the cost estimates and economic evaluations of disease control.

It was necessary to expedite publication of the findings. For this reason, each
chapter of this dissertation was written as an individual paper for publication. Therefore
each chapter has its own set of objectives, literature review, material and methods, and

summary section.

CHAPTER 1

The National Animal Health Monitoring System in Michigan I. Design, data, and

frequencies of selected dairy cattle diseases.

ABSTRACT

A National Animal Health Monitoring System (NAHMS) in Michigan was
started in 1986 to develop statistically valid data for use in estimating disease frequencies
and associated costs in dairy cattle. The objectives of this chapter are to: 1) describe
what was done to implement and maintain the system in Michigan, 2) present selected
disease frequencies, 3) and discuss the epidemiological considerations of what was done
with implications for the results obtained. Veterinary medical officers (VMOS,
veterinarians from the university, state and federal governments) served as data
collectors. Following several sessions of training in current disease and management
problems of dairy cattle, interview techniques, sampling methods, and data collection
instruments, the VMOs participated in selection of the sample herds and data gathering.
Sixty (n=60) of 6,012 dairy herds were randomly selected and the VMOS visited the farms
once a month for 12 months to collect management, disease, inventory, production,
preventive treatment, financial and any other relevant data. Strict data quality control
devices were used. Specific feedback and morale boosting techniques were developed
for the producers and data collectors.

Of the three age groups studied, cows had the greatest number of disease
problems. The top six disorders found more frequently were (from highest to lowest)
breeding problems, clinical mastitis, birth problems, metabolic problems, gastrointestinal
problems, and lameness. In young stock, respiratory, multiple system, breeding problems,
gastrointestinal, lameness, and birth problems were the major problems, while in calves
gastrointestinal, respiratory, multiple system, lameness, Metabolic/nutritional, and

urogenital were the major problem.

INTRODUCTION

Numerous systems of disease monitoring/surveillance have been reported. These
systems vary in five basic ways: 1) sampling design, 2) frequency of data collection, 3)
mechanisms of data collection, 4) measure of disease frequencies, and 5) purpose or
anticipated use of the data. Some monitoring systems have been developed to estimate
prevalence and/or incidence of a single infection/disease. For example, the brucella milk
ring test (USDA Uniform Rules and Methods, 1986) and the market cattle test (Beal,
1977) are strictly for brucellosis in the USA, and the tuberculosis program in the USA
is primarily for bovine tuberculosis (Poppensick and Budd, 1966)

Various monitoring systems are designed to estimate disease frequencies of more
than one disease, but the place of observation and type of measure of disease may vary.
9 Slaughterhouse based monitoring systems, for instance, have been designed primarily to
measure prevalence Of disease conditions as detected at slaughter (Willeburg, 1978; Lloyd
and Schwab, 1987; and the USDA national residue monitoring, 1985)

Some monitoring systems combine information from slaughterhouses and reports
from the farms. These include the disease reports by the Food and Agricultural
Organization and the International Office for Epizootics in France (F AO/IDE, 1975) and
the Inter-American Institute for Cooperation on Agriculture. In the ICE and IICA
monitoring systems, data are Obtained from various ministries/departments of
agriculture/animal industry. These two are passive monitoring systems and, for most
times, the numbers of animals at risk are not known and true rates of diseases cannot
be estimated. In addition, data relating to management, production and cost of disease
are not collected. Furthermore, the sampling and criteria used for data collection are
not very clear. For their intended use, however, these systems provide valuable disease
information on the global and/or regional level.

The Minnesota disease reporting system for food producing animals (Diesch
and Martin, 1979, Diesch, 1983) was an active monitoring system where farm level data
were collected. The herds were selected using proper sampling procedures and the

results, therefore, could be extrapolated to the rest of the state. The animals at risk in

7

most cases were known, so that rates of disease could be computed. In the Minnesota
system, however, management, production, and cost data were not collected.

Since the Minnesota disease program, many farm level monitoring systems have
been developed where multiple diseases, production and management factors were
estimated (Riemann, 1982; Stephens em; Bartlett eLel, 1986; Dohoo and Stahlbaum, 1986;
and Bigras-Poulin and Harvey, 1986). While these monitoring systems included
production, management and cost data, the results obtained may not be generalizable to
the original reference populations due to the type of sampling used. More
comprehensive monitoring systems that involve frequencies of various diseases,
management, production, environment, soil type and social environment of the farms
have been reported (Barnouin and Brochart, 1986; Barnouin, 1986; and Barnouin et_a_l.,
1986). These systems offer variable information on diseases of ruminants and the effects
of environment, and production on observed disease frequencies.

In the USA, a National Animal Health Monitoring System (NAHMS) was started
in 1983; the system was originally called the National Animal Disease Surveillance
System. The NAHMS is a farm level active surveillance system whose goal is to
generate data for statistically valid estimates of incidence and prevalence rates, and costs
of various diseases of livestock and poultry.

A branch of the NAHMS as initiated in the state of Michigan during the 1986/87
calendar year. The objective of the program, in Michigan, was to generate statistically
valid data about dairy cattle health related events, for use in computing national and
state estimates of incidence rates and costs of these animal events. The objectives of
this chapter are to: 1) describe what was done to implement and maintain the system in
Michigan, 2) present selected results, and 3) discuss epidemiological consideration of what

was done with implications for interpretation of the results.

MATERIALS AND METHODS
I . . .

Preparatory steps for initiation of the program started approximately one year
in advance and involved the formation of interdisciplinary planning and management
committees. The committees secured support for the program from: The Michigan
Veterinary Medical Association, Michigan State University (MSU), Michigan
Department of Agriculture (MDA), the US Department of Agriculture
(USDA/APHIS/V S) office in Michigan, Michigan Dairy Herd Improvement Association
(DHIA), and several producer groups. The planning committee, which dealt with policy
matters, and met monthly, was composed of the State veterinarian, the Director of
Animal Industry in the state, the federal veterinarian in charge of Michigan, and an
epidemiologist from the University. The management committee was composed of one
professor of epidemiology, one PhD student in epidemiology, and one veterinarian from
the State Department of Agriculture. This committee coordinated the everyday
activities of the program, including data collection, management and processing.
W

Sixty of the 6,012 available dairy herds were to be selected for participation in
the project. Specific counties, areas within these counties, and the number of herds in
each herd size category to be included in the sample were identified. Herd size data and
maps from the National Agricultural Statistical Service (NASS) and Michigan Crop
Reporting Service (MCRS) were obtained. Using these data, the state was stratified into
the 6 geographical (agricultural) districts and animal density strata. Herds were stratified
according to the number of adult cows available into four size strata - 10-49, 50-99,
100-199, and >200. Because the NAS lists tend to overlook small herds, a List Frame
Selection (LAS) alone would not be appropriate. On the other hand, the use of an Area
Frame Selection (AF S) would pick up the small herds that may not appear on the NASS
list. Using the AFS alone, however, was not viewed as an efficient approach, since too
much time would be needed for the VMOs to physically locate herds. Because of the

aforementioned reasons, both the LAS and AFS methods were used As a result, a

9

sample of 60 herds, based upon probability proportional to animal numbers, was
obtained. Detailed maps with AFS or LAS guidelines and selections were prepared for
use in training of the data collectors and the actual selection of the sample herds.

A total of fifteen veterinary medical officers (VMOs) from the College of
Veterinary Medicine, State and Federal Departments of Agriculture served as data
collectors. The VMOs attended a training session (lasting two days) where interview
techniques, current management practices and common dairy disease problems were
reviewed. Two additional training sessions (each lasting one day) were held. These
two sessions covered: the forms to be used for data collection, the need for probability
based random sampling, the use of area and list frames, and the steps to be followed in
selecting the participating producers.

Wetlands

Each VMO was assigned 2-5 herds, no VMO had more than five. The VMOs
were asked to use be following procedures for the final selection of the herds: 1) contact
the milk inspectors and dairy extension agents in the selected areas to explain the
program, 2) visit with the milk inspectors and dairy extension agents to seek their help
in locating the herds in the specified areas (using the list or area frame methods as
indicated on the maps), 3) confirm the herd sizes with the milk inspector and dairy
extension specialist, 4) write names and addresses of the eligible producers in notebook,
and 5) number the producers serially, ie., from In Each VMO then called the
university epidemiologist to confirm the herd size category and the number of available
herds in that size category. Using a simple random procedure and the information
provided by the VMO, the university epidemiologist selected which particular
producer(s) would be included in the sample. To save time, but at the same time
assuring that every individual producer had an equal chance of being selected, 3-5
numbers were selected and the order in which herds were to be approached was given.
The VMO would go to the first randomly-selected producer and ask him to participate
in the program. If the producer refused, the VMO wrote down the reason for refusal

and approached the next randomly-selected producer.

10

i t ce 0 e ste

All producers who agreed to participate in the program signed an agreement to
keep records for twelve months which assured them of complete confidentiality of
their records. Each producer was paid $25.00 for every month he participated. The
VMOS collected data at the beginning of the program using the initial visit form (Form
1) and provided the farmer with forms (Producer’s Daily Log) to record animal events
during the time between visits. All data collection forms are shown in Appendix A.
The VMO visited the farm monthly and interviewed the producer regarding any animal
events that occurred during the previous month. Data relating to inventory and disease
prevention activities were recorded on Form 2. Data relating to disease (cases, actions
taken to correct them, and consequences of the disease) were recorded on another form,
Form 3. In Michigan, individual cow identification (IDs) were maintained. To maximize
the availability of these individual IDS, a special worksheet (NAHMS VMO worksheet)
was developed. This worksheet was produced for each farm every month. It listed all
the cows on the farm, their most recent calving dates, and any diseases/conditions that
were reported during the previous month. These computer-generated worksheets were
sent to the VMO before the next data collection visit. The VMO worksheets enabled
the VMO to gather data on a case-by-case basis for each individual cow, which should
have improved the ability to identify new cases. Data for completing the
aforementioned forms were extracted from the interviews, producer daily logs, other
sources such as bills, milk receipts, and conversations with the producer’s veterinarian.

All forms were mailed to the Division of Epidemiology at MSU where they
were checked for errors, missing values, proper disease codes, and changes in inventories.
The checking of data was accomplished by veterinary students, graduate students and
faculty in the Division of Epidemiology. Data were entered in microcomputers using
the RzBase System V data base management program. Checks were built in the data
entry process to avoid errors of entry. These check devices would not permit, for
instance, entry of improper disease codes, drug codes, ID, producer code, or wrong

month. After correction for errors on microcomputers, data were copied into files and

11
transmitted to an IBM 3090-180 mainframe computer for storage and analysis.

A monthly report was sent to producers. The report included risk rates of
diseases reported the previous month in the given herd and means of risk rates of the
same diseases Observed in the their herd-size stratum. A six-month report, primarily in
graphics, was provided to the producers. This report included one-month risk estimates
of disease comparing the producer’s herd to the stratum average. A twelve-month (final)
report was given to the producer and this report contained all major findings in that
herd, including estimates of risks of disease, costs of diseases and costs of preventive
measures. A monthly newsletter was used to communicate with VMOS on various issues
of the project, particularly data-quality issues. Examples of the producer reports and
monthly newsletters can found in Kaneene and Hurd, 1987.

O ut tion 'se se re uenc'es 'n Herd

The incidence density (ID) method was used as a measure of disease frequency
for the individual herd for one month (Meittinen, 1976) This method was employed
since there may be a high turnover of animals during a month, since multiple cases can
occur in the same animal within a month and no individual animal data were utilized.
This method is a modified version of the actuarial method discussed by Elandt-Johnson
(1977) (equation 1.1) For this chapter the monthly incidence densities were summarized

into an annual figure (aIDij) for each herd as shown in equation 1.2.

# cases (1.1)

 

animal months

c ses of d' ease du i re t mont
# of animals at
risk at end of - 1/2 withdrawals + 1/2 additions
previous month

5
II

# sold + # died due to ethe; disease

withdrawals

+ # transferred to different age group.

12

# purchased + # transferred in from

additions

other age groups.

'annual" incidence density for the ith herd in the (1.2)
j stratum, expressed per 100 cow years
12

= 2 cases
m=1

aIDu =

 

/12"100
12

2 animal months
m=1

Computation of the mean "annual" incidence density for a stratum is shown in equation

1.3. Procedures for computation of the variances are discussed in Chapter 2.

estimate of the "annual" incidence density for the jth herd (1.3)
size stratum

aIDj

n
I=1
where:

wij = aNARij

 

n
E aNARij
i=1

aNAR = average annual herd size

RESULTS

Sample characteristics of the herds selected are presented in Table 11. Seven of
the producers contacted (10.76%) refused to participate for three reasons:
1) too much work involved in keeping the required data (large herds), 2) lack of interest

3) and family illness.

13

Table 1.1 Projected and achieved Michigan sample characteristics of dairy herds in

 

 

round 1.
Projected
(achieved)
Projected no. of herds
. no. of represented
Herd No. of % of No. of herds in Achieved by each herd
size cattle cattle herds sample # herds In sample
10-49 93,692 27.2 3,283 16 19 205 (173)
50-99 125,353 36.3 1,870 22 18 85 (104)
100-199 94,923 27.5 750 16 12 47 (62)
200+ 31,021 9.0 109 6 5 18 (22)

 

Total 344,989 100 6,012 60 54

Of the three age groups, cows1 had the greatest number of disease problems (Table 1.2)
Calves2 were second in numbers of disease problems (Table 1.3) and the young stock3
had the least disease problems (Table 1.4) Many of the specific diseases reported were
somewhat similar, such as pneumonia and respiratory disease. For this reason many of
the similar disease syndromes were grouped together. The composition of disease groups
are presented in Appendix B. There was noticeable seasonal variation in disease

frequencies, particularly in respiratory and birth problems.

 

lLactating and dry females after first parturition
2Male or female animals from birth to weaning off liquid ration

3Male or female animals from weaning to first calving (females) or first use for breeding
purposes (males).

14

Table 1.2 Most frequently re rted disease problems in Cows, expressed as mean
incidence densities (Ogre standard deviation) per 100 cow years.

 

 

Disease group Strata 1 Strata 2 Strata 3 Strata 4 All strata
Breeding problems 48.98 41.12 27.90 8263 49.85
(4.18) (4.27) (2.42) (5.49) (2.28)
Mastitis 32.71 32.84 3465 31.98 33.05
(3.99) (3.32) (2.25) (3.38) (1.64)
Birth problems 9.22 17.08 11.51 14.37 13.80
(1.86) (2.57) (1.65) (2.37) (0.79)
Metabolic/nutrition 7.21 7.54 4.96 20.37 1021
(1.66) (1.59) (113) (2.84) (0.89)
Gastrointestinal 12.91 4.95 4.76 9.42 726
(2.08) (1.74) (1.12) (1.88) (1.23)
La meness 4.36 10.28 5.06 4.66 6.61
(1.70) (1.85) (1.00) (1.51) (0.39)
Multiple system 5.87 6.06 556 3.90 5.34
(1.63) (1.95) (1.36) (1.24) (085)
Urogenital system 687 7.69 1.68 3.04 484
(2.04) (2.02) .87) (1.07) (0.81)
Respiratory 4.02 1.33 1.68 1.52 187
(1.66) (1.09) (.83) (.74) (0.74)

 

15

Table 1.3 Most frequently re orted disease problems in Calves, expressed as mean
incidence densities (zine standard deviation) per 100 animal years.

 

 

Disease group Strata 1 Strata 2 Strata 3 Strata 4 All strata
Gastrointestinal 40.88 61.18 31.65 230.76 79.74
(388) (5.42) (5.52) (11.76) (4.76)
Respiratory 4088 42.03 2839 67.69 42.40
(2.48) (4.76) (3.45) (5.10) (2.66)
Multiple system 2484 12.07 5.12 6.92 11.27
(4.91) (2.72) (2.05) (1.72) (L74)
Lameness 0.0 .41 0.0 .76 0.28
(0.0) (0.57) (0.0) (0.69) (0.26)
Metabolic/nutrition 0.80 .42 0.0 0.0 0.28
(0.88) (1.18) (0.0) (0.0) (0.45)
Urogenital 0.0 0.0 .46 0.0 0.14
(0.0) (0.0) (0.67) (0.0) (0.13)

 

Table 1.4 Most fre uently reported disease problems in Young Stock, expressed as
mean incrdence densities (one standard deviation) per 100 animal years.

 

 

Disease group Strata 1 Strata 2 Strata 3 Strata 4 All strata
Respiratory 0.66 8.21 3.70 6.20 555
(0.65) (2.86) (1.75) (1.99) (0.79)
Multiple system 2.65 1.76 0.13 2.12 1.60
(1.36) (1.26) (0.38) (0.61) .61
Breeding problems 088 0.83 0.53 2.00 1.09
(087) (0.74) (0.41) (L09) (0.39)
Gastrointestinal 3.10 0.58 0.13 0.0 0.66
(1.49) (085) (0.24) (0.0) (0.65)
La meness 0.66 0.33 0.0 0.22 027
(0.65) (0.48) (0.0) (033) (0.28)
Birth problems 0.0 0.08 0.0 0.11 0.06
(0.0) (0.30) (0.0) (0.27) (0.00)
Mastitis 0.0 0.0 0.13 0.0 0.03
(0.0) (0.0) (0.24) (0.0) (0.07)

 

16

DISCUSSION

Preparatory steps taken during the initiation phase seemed to have been useful
in obtaining industry, professional, and political support within the state. Such support
minimized the logistics of implementation and maintenance of the system and would
appear to be mandatory for any state wanting to implement NAHMS. All the groups
contacted during the preparatory phase wanted to know if there was a real need for a
NAHMS and how they would benefit from such a system. The herd statistics from both
the NASS and MCRS seemed to have been satisfactory for use in the design of the
sample, particularly when both list and area frames were used. However, to maintain
a random sample based upon probability proportioned to animal numbers it was
essential for the VMOS o confirm location and sizes of herds. This is because size of
herds change from time to time. The fact that one person picked the final herds (as
opposed to each VMO picking their own) produced consistency, and helped to maintain
randomness.

Feedback from all the VMOS indicated that the training received was essential
and should be an ongoing program within NAHMS. It was through repeated training
that the need for random sampling, minimizing information bias (and other biases), and
understanding the data collection instruments was appreciated. The VMO worksheet
(as determined by a percentage of corrections made) was a very useful instrument for
cross-checking with data recorded on the general NAHMS forms. Additionally, it
enabled the VMO to prompt the producer to remember specific events on specific cows,
since this worksheet had individual cow identification. Data quality has and will always
be an important issue in field studies (Anderson, 1982) In the Michigan experience, data
quality was a function of confidentiality assurance to the producers, feedback
information to producers, morale of the VMOS, and critical checking of the data.
Because producers were assured confidentiality of their records, most producers were
willing to record various events on the farm, including drugs used and financial aspects

of their farms. All VMOS indicated that the monthly and semi-annual reports

17

encouraged the producers to record events on their farms. The producers particularly
liked comparing themselves to other herds of the same herd-size stratum. These reports
to the producers, however, should be as simple as possible and mostly in graphics. The
VMOS had a very delicate role in that they had to sell the program to the producer,
probe the producer for data and clarifications, record the data accurately, interact with
the producer’s veterinarian and interpret the monthly, semi-annual and annual producer
reports. It was, therefore, essential for them to be motivated. The morale-boosting
mechanisms used (see Material and Methods section) were effective in maintaining
and/or increasing the VMOS’ morale. Of particular value (according to the VMOS
assessment) were the group sessions held. These resulted in open discussion.
Additionally, the VMOS indicated that seeing the monthly, bi-annual and annual
producer reports boosted their morale. They could see the results of their efforts, the
scientific value of the data, and had tangible products to show to their producers.

The availability of individual cow identifications was helpful in confirming new
cases. These data will be helpful when we examine the relationships of various risk
factors to specific disease frequencies. In an active surveillance like this one where all
producers are asked to record all possible disease conditions, it is efficient to report
disease frequencies in terms of groups of disease entities. Since definitions of disease
entities may vary from system to system, results reported in this chapter may not be
directly comparable to those reported elsewhere. Several methodological issues
regarding computation of disease frequencies were raised in Michigan. Since these issues
may be of great value to NAHMS as a whole and to epidemiologists in general, the

second chapter of this dissertation addresses these issues.

CHAPTER 2

The National Animal Health Monitoring System in Michigan 11: Methodological issues
in the estimation of frequencies of disease in a prospective study of multiple dynamic

populations.

ABSTRACT

Procedures for the computation of disease frequency measures and their
associated variances from data collected through prospective study of multiple dynamic
cohorts (herds) with a National Animal Health Monitoring System, are proposed.
Estimates of the annual incidence density for a group of herds or the one month risk
of disease can be calculated from the same within herd measure of monthly incidence
density.

It is proposed that the choices regarding which measure to be estimated depends
on the intended use of the information. Risk estimates are appropriate for producers
and clinical health professional making decisions at the animal or herd level. Incidence
density measures are appropriate for purposes of extrapolation to populations for state

and regional level decision making.

INTRODUCTION

Disease monitoring activities in livestock populations can take on a variety of
forms, with a variety of goals and users (Beal, 1983) Some activities observe prevalent
cases of disease at slaughter (Willeburg, 1978, Lloyd and Schwab, 1987) or upon
submission to a diagnostic laboratory (Davies, 1978) Other activities might observe
disease occurrences as a result of ongoing herd management and disease control
programs (Stephens, ele, 1982, Bartlett, 9131., 1986, Dohoo and Stahlbaum, 1986). The
shortcomings of these activities for gaining estimates of disease frequency that are

statistically valid, hence useful for extrapolation to a source population, have been

18

19

discussed (Beal, 1983) Efforts to overcome these shortcomings have resulted in the
antecedent Minnesota Food Animal Disease Reporting System (Diesch, 1983) and the
present National Animal Health Monitoring System. These projects are unique inthat
herds are purposefully selected for follow-up. In these situations, multiple cohorts
(herds) are repeatedly observed in a prospective longitudinal study for the purpose of
obtaining a sample estimate of disease frequency that can be extrapolated, with defined
confidence limits, to a reference population at the state, regional, or national level.

By comparison, most follow-up studies in human epidemiology involve
observations on only one or two cohorts of individuals. The purpose of these studies
is usually hypothesis testing about the effect of an exposure or risk factor on the
occurrence of disease in an individual, not the estimation of a population parameter
(Kleinbaum, e;_a_1., 1982, Susser, 1985) Consequently, most statistical procedures have
been developed around estimation and variance calculations of these effect measures,
such as the risk ratio, odds ratio, and the risk difference. (Fliess e_t_el.; 1976, Rothman,
1986). In animal populations some work has been done in regards to estimating the
prevalence of disease (Beal, 1985; Farver et_e1., 1985); however, this may not be directly
applicable to incidence data from follow-up studies (Chiang, 1961).

Estimation procedures, that can be consistently applied to estimate the frequency
of disease in a population consisting of multiple dynamic subpopulations (herds or
cohorts), need to be documented. Since NAHMS is a national effort in the United
States, it is important that these and other methodologies be standardized in order to
provide for comparability between states. The objectives of this chapter are to: I) raise
the issues involved with disease frequency estimation, 2) propose a criterion for
determining the appropriate disease frequency measure to be estimated, and 3) propose

methods for computing sample estimates and variances of these frequency measures.

20
METHODS
s e i d t co e '

Sixty (60) of the 6,012 dairy cattle herds in Michigan were randomly selected for
one year of follow-up. A detailed account of the selection of these herds, data collection
tools, and the data collected are presented in Chapter 1. Individual animal information,
such as calving date and age were collected in the Michigan project. However, since this
information is not usually collected in the standard NAHMS design, it will not be
considered in this chapter.

Warm

Two general types of disease frequency have been recognized, the risk rate and
the true rate or incidence density (Martin, M. 1987; Bendixen, 1987b; Klienbaum eLeI,
1982) We propose that choices regarding the type of measure, to be estimated from a
NAHMS, depend on the intended use of the estimates, with constraints based on the
type of data available. Incidence densities are useful for population estimates and macro
decision making by state and national level policy makers. The risk rate is useful for
selecting appropriate treatments, and for personal decisions regarding health related
behaviors, in other words, micro level decision making by producers and clinically
concerned health professionals.

The incidence density is a meaningful measure of the experience of the
population group (Chiang, 1961), and as such is more appropriate for extrapolation
(Alderink, 1986) Leech (1971), when discussing disease monitoring systems in Britain,
comments that incidence density measures are more meaningful than risk estimates.
The animal disease surveillance program in Minnesota estimated disease frequency as
incidence densities (Diesch, 1983), and incidence densities of mastitis have been reported
by Bendixen (1988) However, the incidence density has no application at the individual
animal level, and is not very useful to a producer or clinical epidemiologist (Miettinen,
1976, Bendixen, 1987b) The exception to this statement is when incidence density
measures are used to determine the relative risk of a given exposure. Morgenstern et

a1. (1980) defined risk as the conditional, a pziori, probability of disease occurrence in an

21

individual. Risk estimates of common dairy cattle diseases have been reported by many
investigators (Bartlett, etel, 1986; Bendixen, 1987a; Curtis ml, 1988; Dohoo e_t_el_., 1983;
Erb, 1984; Martin et_el., 1975; Simensen, 1982; Waltner-Toews, 1986) Although some of
these reports may use the term ”incidence rate”, examination of the calculations Show
that the measure is actually a risk. These reports are generally aimed at the producer
or the clinician and relate to the question of how individual factors may affect an
animal’s risk of disease. These risk estimates might be useful for decisions regarding the
implementation of some intervention, such as a vaccination program, which must include
consideration of the expected probability (ie. the risk) that an animal and/or herd will
be infected.

Bendixen (1987b) discusses how the type of data constrains the choice of measure
to be estimated. The risk, or cumulative incidence is appropriate for fixed populations
and some dynamic populations if the risk period is well defined. The incidence density
is appropriate for dynamic populations when disease occurrence is not restricted to a
specific time. The latter applies to data from the NAHMS.

rd al atio d'se e f e uenc

Calculation of the frequency of disease in a given herd, for a given month can
be implemented in a variety of ways, depending on whether the population at risk is
assumed to be of fixed size during the observation interval or of changing size. If the
population is fixed or animals are at risk for a definable time period or proportion of
animals affected, the risk can be calculated (Klienbaum gel, 1982; Elandt-Johnson, 1975)
This number represents the risk of disease for a given time period. The risk is
conditional on new animals not entering the population and that only one occurrence
of the disease per animal is being considered.

In a situation, such as NAHMS, the population size may change dramatically
during the observation period, and animals can be affected more than once. The former
instance was particularly true for calves in the Michigan experience. In this situation,
the incidence density is recommended (Bendixen, 1987b; Klienbaum mi, 1982; Miettinen,

1976; Rothman, 1986) Also in cases where individual animal data are not available, it is

22
not possible to calculate measures such as the lactational incidence rate or periparturient
risk rates, as it is not possible to determine which animals have recently calved and are
at risk. The formula for the incidence density (IDijm) for one disease, for one month,
for the it“ herd, in the jth stratum is shown in equation 2.1. This is a modified version
of the actuarial method as shown by Elandt-Johnson (1977)

Incidence densities for some diseases may be biased downward due to the
inclusion of animals in the denominator that are no longer at risk for that particular
disease. Due to the nature of the data collected, all animals in the herd, in a given age
group, contribute to calculation of the animal months. Collection of individual
information, for all age groups would allow for better estimation of frequencies as well
as providing better data for research applications such as identification of important

individual risk factors.

 

# cases (21)
animal months
cases 0 disease du 'n cur ent o h
IDijm = # of animals at
risk at end of - 1/2 withdrawals + 1/2 additions
previous month
withdrawals = # sold + # died due to other disease
+ # transferred to different age group.
additions = # purchased + # transferred in from
other age groups.
Populatieg estimates 9! angge! igejdence

Since it has been proposed that the incidence density (true rate) is the most
meaningful expression of disease frequency for macro level decision making, the
calculation of a population estimate of this measure will be discussed. For population
estimates of disease, it may be reasonable to aggregate the results of monthly
observations into one annual figure for each herd. The monthly incidence densities

(IDijm) are easily aggregated as shown in equation 2.2 (Rothman, 1986) This term will

23
be referred to as the ”annual" incidence density (aIDij) which is not as accurate as
calling it the incidence density expressed in terms of animal years, but is more
convenient. This annual incidence density (aIDij) represents the average force of
morbidity observed over one year of repeated monthly observations. It assumes a
constant rate of disease for the entire year, hence seasonal fluctuations are ignored.

This may present a problem as some diseases did exhibit noticeable seasonal fluctuations

(Kaneene and Hurd, 1989)

aID-- = "annual” incidence density for the ith herd in the (2.2)
jt stratum, expressed per 100 cow years

12
= 2 cases
m=1
/ 12 " 100

 

12
2 animal months

m=1

If the annual incidence density (aIDij) represents the unit of measure for one
herd, then a summarization of the frequency for many herds is required in order to
estimate the rate for a population. It is proposed that the data should be stratified
according to herd size (Beal, 1985), since this is assumed to affect management and
comparability of disease rates. For this reason, discussion of the summarization of rates
will not proceed beyond the herd size stratum (j) level, although an overall frequency
estimate is estimable if desired. The average stratum specific annual incidence density
(aIDj) is computed as in equation 2.3. It is the weighted average of the herd specific
annual ID’s (aIDij) The weights are those used in standard sampling theory for
estimation of proportions (Cochran, 1977; Levy and Lemeshow, 1980) Other weights
could be considered, (such as the inverse of the variance) since the incidence density is
not a binomial proportion (Klienbaum, 1982; Rothman, 1986) It is also reasonable that
a finite population correction factor (nj/Nj), for the herd sampling, should be considered;
however, this was dropped since the number of herds sampled (nj) was relatively small

compared to the number of herds in the state (Ni) This also simplifies the equations

24

for discussion.

aID- = estimate of the ”annual" incidence density for the jth herd(2.3)
size stratum

D

 

i=1
where:
n
2 aNARij
i=1

n = number of herds in j‘h stratum

aNARij = number of animal years = a ima o s
12

Vaigiaiiee estimates 91 annual ieeigenee

If one views the multistage sampling procedure as a cluster sample, where herds
are the clusters, then variation will be contributed from within herds and between herds
(Alderink, 1986; Beal, 1985; Farver, 1987) However, it might be argued that, since we are
observing all the animals within the herd for disease, there will be no within herd
variance in the aIDij. This is equivalent to saying that we have perfect knowledge of
the rate of disease in that herd and that it is not subject to any random variation.
Chiang (1961) suggests that we are considering a stochastic phenomenon (disease) which
is subject to chance and as such a within herd variance should be considered.

Since the incidence density (aIDij) is not a binomial proportion, nor is it a
probability function, it’s variance must be approximated by it’s relationship to the
probability (risk) of disease in a given herd. The relationship of incidence density to
risk for a given period has been described as shown in equation 2.4 (Morgenstern e1_ai.
1980) Application of this functional relationship results in a variance estimator for aIDij

as shown in equation 2.5. Annual number at risk (aNAR) represents the average number

of animals in' the herd for the year. The variance of the average annual incidence

25
density S (aIDj) for the jth stratum is a tunction of the weighted individual herd

variances S (aIDii) and the between herd variances as shown in equation 2.6.

 

 

 

Risk = 1 - exp(-ID) (2.4)
aID-- [I - (1 - exp (-aID.- )]
32 (aIDij= ” ") (25)
aNAR
= Sample estimate of the variance of the "annual" incidence
density for it herd in jt stratum
2 animal months
aNARij = number of animal years =
12
__ n _ n
Sz(aIDj) = 2 (aIDij - 211D)2 + Ewij2 S2(aIDij) (2.6)
i=1 i=1
“i
= sample estimate of the variance of the "annual" incidence density
Where:
nj = # of herds in jth stratum
st' t'o

An estimate of the probability of occurrence of a disease on a farm should
aid producers in planning health care and other management changes. The risk estimate
must be defined for a specific time period, for example the one month risk of disease,
the one year risk, or the lactational risk. For some diseases the one month risk (Riim)
will vary seasonally. Since these risk estimates were reported to the participating
N AHMS producers they were not aggregated over time. Therefore, equations shown are
for stratum estimates of the one month risk (Rim) and it’s variance.

The one month risk (Rijm) for a given herd can be approximated from the

incidence density for one month. If the IDijm is less than 0.10 and the time period is

short, the risk and ID can be assumed to be equal (Klienbaum, et el, 1982; Erb, 1984)

26

If these assumptions do not hold, the risk can be approximated using equation 2.4. In

most cases, in Michigan, these assumptions held true, but occasional outbreaks of

diarrhea and respiratory disease in calves did result in large ID’s some greater than 1.0,

which is acceptable for the incidence density measure (Rothman, 1986) Therefore the

conversion in equation 2.4 is recommended as a routine procedure for NAHMS. An

estimate of the stratum one month risk (Rita) and it’s variance (82(ij)) can proceed, as

in equations 2.7-210, treating the risk as a binomial proportion (Elandt-Johnson, 1977;

Martin, 1987) Use of the cluster method for computing a variance should be considered

(Beal, 1985), but one is then forced to assume that Riim represents an observed number

of positive cases out of an observed number of sampled cases.

”a

um

Where:

52 (R...)

82 (RH...)

Where:

iim

Where:

one month risk of disease (X) for the ith herd in the jth
stratum, for the ant month

IDijm same as equation 2.1

Rijrn (1 ' Rijm)

 

mij'n'l

sample estimate of the variance of
the risk from the ith herd in the

jth stratum for the mth month.

hypothetical number of animals at risk
in the ith herd in the it“ stratum for
the Int month.

mean one month risk of disease (X) for the ju' stratum for
the mth month only

(27)

(28)

(29)

27

mm
2 mm
n
i=1
i = 1-n; n a number of herds in the jth stratum
n n 2 2
52min) = if (Rm - Rim): + ivy? S (Rm) (210)

 

“1

sample estimate of the variance of Rim

n. = # of herds in j“ stratum

Further summarization of the stratum risk (Rim) estimates, could be accomplished
in two separate ways: computation of a mean one month risk for 12 months of
observations (R1), and computation of an annual risk of disease (annR) The mean
monthly risk for one year of observation could be computed as the sum of all the
weighted mean risk estimates (Rim) divided by the number of months of observation.
This will represent the average one month risk of disease; it’s value may be limited as
this measure tends to ignore the fact that multiple cases of disease can occur in the same
animal and that the occurrence of disease in an animal or risk (Riim) for a herd may not
be independent from one month to the next. Computation of a variance for these risk
estimates is not meaningful since the risk is likely to vary significantly within that 12
months of observation due to seasonal effects, versus random variation.

The annual risk of disease (annR), which could be a valuable measure, would
be computed according to equation 2.11 (Kleinbaum, e_t_e_i., 1982) This measure is only
appropriate if animals are at risk for the entire 12 month period. This does not apply
for calves which mature into different age category, or for periparturient cow diseases.
For diseases with a limited risk period, the annual risk (annR) will probably be an
inaccurate since the model assumes animals are at risk for the full 12 months and the

risks are derived from IDs which are biased downward for these diseases.

28

12
annR = 1 - 1r (1 - Rim) (2.11)
=1

CONCLUSIONS

The choice of the most appropriate disease frequency measure to be estimated
from a National Animal Health Monitoring System is primarily user dependent. A set
of calculations have been proposed in order to provide for standardization of frequency
computations. All the various estimators are derived from the incidence densities
calculated from a from herds randomly selected and observed monthly for a period of
time, in this case, one year. The progression of each of these measures from the
incidence density (IDm), is in shown in figure 2.1. Suggested uses of each measure are
also shown. Other progressions could be considered, but these were chosen based on
their anticipated use and approximatable statistics. Further work is needed in the areas
of 1) improved ways to calculate the IDijm so as to remove bias, 2) determining the most

appropriate weighting term for stratum estimates, and 3) calculation of the variances.

«2
P «we a «nu Afimv N u «emu

an“ ~_ prhammv w

 

«mane—umo
.aco.uu= go I
moans—umo com.aan5ou .
_o=o_uu: Lo» I Acumauc. go» I memo»
«ache A gauche” A you c. uummoeaxo A
II n a. not»; at»; a. as» as.
“we o—u cage I “nun hu—mcuu oucou.u=. I n.a_o
Av
Az
As..a~.
sauce «co co;
zu_m=uo
a > o e I
u PneuWDM_g_w macaw—u:—
c. aces; .wo
Co m=o_ua>LOmao
Nu Soc. xm_e
sagas use case I «an can.cnn5ou
Louauoen an» I Louauoaa
engage» a A a» uuueaaoa I A
2353 «A :n «5 E 33.. “we Eu: u . .3 E.
Lee 8a.; an Eco x».c gazes 0:0 I saw xm_e g» oco I .z

wgmno 550.5...

g a c. «can:
.3.— ..m L 5:272 I

mecca

Flow chart of various disease frequency measures proposed, with

(I expected use.

ion an

t

rni

def

Figure 2.1 -

CHAPTER 3

The National Animal Health Monitoring System in Michigan III. Cost estimates of

selected dairy cattle diseases

ABSTRACT

A study was conducted to estimate costs of major dairy cattle diseases. Sixty
(n = 60) of the 6,012 dairy herds in Michigan were stratified and randomly selected for
participation in the National Animal Health Monitoring System in Michigan.
Government and university veterinarians visited each herd once a month for a total
period of 12 months. At each visit data relating to diseases, production, management,
finance, treatments, preventive activities, animal events, and any other relevant events
were collected.

Monthly and annual cost estimates of disease treatments were computed in each
herd and stratum. Similarly, monthly and annual estimated preventive costs were
estimated. Results were expressed as cost per head and given separately for cows, young
stock, and calves. In cows, the most expensive seven disease entities were: 1) clinical
mastitis, 2) breeding problems, 3) gastrointestinal problems, 4) birth problems, 5) multi-
system, 6) lameness, and 7) metabolic/ nutritional diseases (1 being the highest and 7 the
lowest) In terms of estimated annual preventive cost, however, the ranking of the seven
disease entities were (from highest to lowest): 1) Mastitis, 2) breeding problems, 3)
lameness, 4) birth problems, 5) multi-system, 6) gastrointestinal disease, and 7)
metabolic/nutritional problems.

In young stock, the mostly costly diseases were the multiple system problems,
breeding problems, respiratory disease, birth problems, gastrointestinal, and lameness.
In calves, the most costly disease problems were gastrointestinal problems, respiratory

diseases, multiple systems, birth problems, metabolic diseases, and lameness. Methodo-

3O

31

logical issues, as they relate to data collection and estimation of costs as well as

suggestions for improving the accuracy of these estimates, are discussed.

INTRODUCTION

In Chapter 1, the National Animal Health Monitoring System (NAHMS) in
Michigan was described in relation to the design of the project, data collection and
observed frequencies of dairy cattle disease. In Chapter 2 methodological issues in the
estimation of frequencies of diseases in a prospective study of multiple dynamic
populations were discussed. In the present chapter, cost estimates of dairy cattle disease
observed in a 12 month period will be discussed.

Interest in the economic effects of diseases and the related control/prevention
activities has been increasing in the last 15 years. Many studies have focused on the
economic effect of one disease entity. These have included: mastitis (Janzen, 1970;
Pilchard, 1972; Natzke, 1976; Dobbins, 1977; Blosser, 1979, Fetrow e_t_a_i, 1980, 1987; and
Kirk and Bartlett, 1988), reproductive problems (Speicher and Meadows, 1967; Louca and
Legates, 1968; Pelissier, 1972; Esslemont, 1974; Olds e_t_a_l, 1979, James and Esslemont, I979,
Holmann et_al_; 1984; Dijkhuizen e131; 1985(a); 1985(b); Bartlett PM» 1985, 1986(3), 1986(b);
Slenning, 1986; and Marsh e;_a_i, 1987) Some studies have reported on the economics of
a single agent caused disease (Goodger and Skirrow, 1986; Kliebenstein eLel, 1986; Hallam
_e_t_ei, 1986) Only limited reports on economics of disease control and prevention have
been found in the literature (Grunsell e_t_ei, 1969, Barfoot et_el, 1971; Morris, 1971; James
and Ellis, 1979, Goodger and Kushman, 1984/85; Ellis, 1986; Alderink, 1986; Hallam, gel,
1986; Alderink and Kaneene, 1987)

The literature, however, is virtually devoid of reports where costs of production
diseases (non-regulatory) were estimated using data from an active surveillance program
like NAHMS. The objective of this chapter, therefore, is to report on cost estimates of

production diseases. Specific aims of the chapter are to: 1) describe the methods used

32
in estimating costs of diseases, 2) critically evaluate the results in relation to the data
and methods used in the cost estimates, and 3) offer some suggestions for improving the

accuracy of the cost estimates.

MATERIALS AND METHODS
Design, date eollection see data quality eontrol techniques

The design, coordination, data collection, and data quality techniques used were
described in the first chapter. Briefly, 60 dairy cattle herds were randomly selected to
participate in the program. Veterinary medical officers (veterinarians from the
university, state and federal departments of agriculture) visited the herds once a month
and collected data for a period of 12 months. The forms used to collect preventive
measure costs and to collect other disease related costs are shown in appendix A.

st' tion f monthl cost 0 a disease in a erd
Assume that the disease in question was X in a herd i, stratum j for the month

In. The monthly total cost TC(X)ijrn was then estimated using equation 3.1.

TC(X)ijIn = Drug(X) + Vet(X) + Labo X) + Cull(X) + Dead(X) + (3.1)
Dead calf(X) + Milk loss(X
Where:
Dru (X) = Drug cost of disease (X) treatment
Vet X) = Veterinary expenses for disease (X) treatment
Labor(X) = Hours spent treating the disease (X) multiplied by a
standard wage of $550 (Nott et al, 1986)
Cull(X) = Net cull costs for disease (X)
Net cull cost = Replacement value -net salvage
value
Replacement = Replacement cost for an animal of
same age and genetic potential
Net salvage = Salvage price less transportation and
any other related expenses
Dead (X) = Replacement cost (as defined Cull) plus disposal fees

Dead calf(X) = Value (as reported by producers) of calves born dead
due to the disease (X) in the darn (This figure did not
include calves that were affected with the disease and
died. These figures were reported separately

Milk loss(X) = (lbs loss x price per month) - (lbs loss x % fed to calves)
x (replacer price)

33

Preventive(X) = Monthly cost for preventing disease (Computed as annual
total for each herd then divided by number of months
to give a monthly cost.

0 ' t 0s 0 a is as
This estimate was computed in two steps. The first step was to determine the

cost of a disease per head, for one month, in a given herd using equation 3.2. This

included preventive and treatment costs.

 

 

C TC(X)ijm (32)
"m # of animals at risk # of animals at risk
at end of previous month + at end of this month
2
Where:
TC(X)i- =the new dollars incurred from incident and prevalent cases

i' = cost per head in the i hherd in the j hstratum for the m h month
"al’mrisk" = all animals of the specific age group minus nonrecovered cases from the
previous month

The next step was to use the values estimated in equation 3.2 and estimate a

weighted monthly mean cost of a disease per head using equation 3.3.

2 (Cijm
i=1

min.)- (33)

 

Where: mijm = Number of animals at risk in the ith herd in the jth stratum for the
mth month estimated from the denominator of equation 3.2, i = I to n,
n = number of herds in the j stratum

A ua isease costs or ive 'sease
This figure was the sum of all the monthly means and was expressed on a per

head basis.

12
Annual costs= 2 ij (3.4)
m=1

Amiga] preventive eosis

The annual costs of preventing disease (X) were computed for each herd by
taking the total expenditures for one year preventive measures. This includes activities

such as dry treatment, vaccination, and associated labor.

RESULTS

The disease/problems were grouped for expressing and comparing results, and
these groupings are presented in Appendix B. The estimated annual costs Of disease in
Cows, Calves, and Young Stock are presented in Tables 3.1, 3.2 and 3.3, respectively.
Similarly, the estimated annual costs of prevention in the three groups are presented in

Tables 3.4, 3.5 and 3.6.

35

Table 3.1 Total dollar cost of disease per COW per year (including cost of prevention)

 

Herd Size Strata

 

Disease Group Stratum 1 ‘ Stratum 2 Stratum 3 Stratum 4 Overall
Mastitis 38.22 39.29 2872 35.73 3554
(000-12460)‘ (5.65-6819) (177-15485) (529-5494) (0.00-15485)

Breed 24.98 26.46 21.25 24.70 24.46
(0.00-6613) (4.02-61.66) (2.30-3167) 097-3372) (000-6613)

GI 23.23 6.28 8.09 13.40 11.13
(0.00-3670) (0.00-1835) (043-1957) (002-2458) (000-3670)

Birth 10.29 14.92 1.75 989 9.60
(000-4366) (007-4253) (000-1355) (112-14.76) (000-4366)

Multi 14.55 7.72 4.46 809 801
(0.00-6783) (000-3078) (0.28-26.39) (020-1982) (0.00-6783)

La meness 9.00 9.79 0.10 818 6.81
(0.00-1822) (0.00-3088) (0.00-1841) (000-1445) (0.00-3088)

MetaNutr 8.27 682 3.12 6.53 6.03
(000-1957) (000-2138) (030-2664) (149-1075) (0.00-2664)

Resp 2.36 1.65 10.45 1.56 3.95
(000-2403) (000-742) (000-412) (0.16-4.57) (000-2403)

UroGen 6.89 3.94 0.04 1.65 2.80
(0.00-3841) (000-1312) (00048.36) (0.05-3.97) (0.00-4836)

 

“ = Minimum and maximum values.

36

Table 3.2 Total dollar cost of disease per CALF per year (including cost Of prevention)

 

 

W
Disease Group Stratum 1 Stratum 2 Stratum 3 Stratum 4 Overall
Mastitis 24.92 3832 809 74.60 33.46
(000100.00)‘ (000261.53) (000-15000) (1801-34592) (000345.92)
Resp 17.41 10.64 10.45 2667 14.71
(000117.00) (000119.16) (000114.86) 0.003671) (000119.16)
Multi 29.11 14.46 4.46 3.52 11.15
(000236.22) (0.007388) (00020.57) (00023.78) (000236.22)
Birth 5.41 4.18 1.75 152 3.17
(00013.53) (00012.31) (0.001603) (00011.42) (0.001603)
MetaNutr 0.13 0.70 0.08 605 1.39
(0001.84) (0004.08) (0.000.60) (0.002646) (0.002646)
Lameness 0.00 002 0.10 0.08 .05
(0.000.17) (0001.14) (0000.44) (0001.14)
Uro gen 0.00 0.04 0.04 0.00 0.01
(0000.93) (0000.27) (0000.93)

 

"' = Minimum and maximum values.

37

Table 3.3 Total dollar cost of disease per YOUNG STOCK per year (including cost of
prevention)

 

 

' e t a

Disease Group Stratum 1 Stratum 2 Stratum 3 Stratum 4 Overall
Multi 5.91 3.33 0.93 4.49 3.45
(00024.45)‘ (00041.40) (00011.25) (00014.52) (00041.40)

Breed 188 1.07 2.02 4.78 2.41
(0.002084) (0.00386) (0005.03) (00011.90) (0.002084)

Resp 1.21 0.90 1.65 3.98 1.95
(0004.69) (0004.94) (0003.35) (0709.25) (0009.25)

Birth 1.41 1.20 1.10 2.07 3.17
(0005.56) (0002.73) (00019.06) (024-573) (00019.06)

GI 1.21 065 1.14 0.17 0.71
(0.001646) (0.00848) (0004.15) (0.000.78) (0001646)

La meness 0.31 0.05 0.03 0.02 0.08
(0003.21) (0.000.64) (0.000.14) (0000.04) (0003.21)

MetaNutr 0.01 0.03 0.02 0.00 0.02
(0.000.18) (0.000.45) (0001.68) (0.001.68)

Mastitis 0.01 0.03 >000 0.00 0.01
(0000.23) (0.000.45) (0.00002) (0.00045)

 

" = Minimum and maximum values.

38

Table 3.4 Annual cost of preventive measures of the top 10 disease problems of COWS
(expressed as mean US. dollars per cow)

 

EELCLSIZEStr—ata

 

Disease
Group 1049 5099 100199 200+ Overall
Mastitis 2.45 6.50 331 4.45 456
(00013.04)‘ (0.99-2813) (0.19-870) (134-679) (0.002813)
Breed 3.11 4.36 3.70 3.97 3.91
(0.001584) (00012.86) (0.43-653) 0005.92) (0.001584)
Lameness 1.38 1.45 0.64 437 2.00
(00012.20) (0.00632) (0.00381) (0.001056) (00012.20)
Birth 0.47 1.36 0.28 030 0.68
prob (000669) (0001686) (0001.38) (0.000.71) (00016.86)
Multi 0.17 0.17 1.10 0.13 0.39
system (0002.79) (0001.08) (0009.91) (0000.55) (0.009.91)
GI 0.43 0.22 0.15 0.75 038
(0005.78) (0001.24) (0000.84) (0001.40) (0.005.78)
MetaNutr 0.44 0.43 0.11 0.49 0.37
(0002.81) (0.005.88) (0.00-044) (0001.85) (0.00588)
Resp 035 032 0.42 0.36 0.36
(0004.45) (0001.47) (0002.61) (0.16-1.00) (0004.45)
Inte g 0.26 050 0.00 0.00 0.21
(0002.33) (0.00-632) (0.00-632)
UroGen 0.14 0.00 0.00 0.00 0.02
(0.00112) (0.00112)

 

‘ = Minimum and maximum values.

39

Table 35 Annual cost of preventive measures of the to 8 disease problems of

CALVES (expressed as mean US. dollars per calf

 

Llerd Size Strata

 

Disease

Group 10-49 5099 100199 200+ Overall

GI 0.96 3.67 1.85 5.29 2.94
(0.004.95)‘ (0.002337) (00027.03) (0.002804) (0.002804)

Birth 1.84 2.70 1.04 1.47 1.82
(0.00873) (00010.65) (0002.74) 0.00-836) (0.001065)

Resp 1.13 0.07 2.23 4.08 1.64
(00010.69) (0002.53) (0009.14) (00011.40) (00011.40)

MetaNutr 0.04 037 0.08 534 1.14
(0000.67) (0004.08) (0.000.60) (00019.16) (00019.16)

Multi 055 056 1.69 0.09 0.82
(00012.97) (0.001080) (0.00693) (0.00039) (00012.97 )

Inte g 0.00 0.09 0.00 0.02 0.03
(0001.39) (0000.08) (0001.39)

Lameness 0.00 0.00 0.07 0.00 0.02
(0.000.40) (0.000.40)

Uro gen 0.00 0.04 0.00 0.00 0.01
(0.000.93) (0.000.93)

 

" = Minimum and maximum values.

Table 3.6 Annual cost of preventive measures of the top 8 disease problems of YOUNG
STOCK (expressed as mean US. dollars per animal)

 

Herd Size Strata

 

Disease

Group 10-49 5099 100199 200+ Overall

Birth 0.90 1.20 0.48 0.68 086
(0.00556)‘ (0002.73) (025-117) (0001.13) (0.00556)

G1 0.31 053 0.33 0.20 036
(0001.68) (0003.40) (0001.40) (0.000.78) (0.003.40)

Resp 0.37 0.24 0.30 0.22 0.27
(0002.82) (0.000.92) (0002.25) (0.000.75) (0.002.82)
Multi 0.21 0.41 035 0.00 0.26
(0001.42) (0002.75) (0002.21) (0002.75)
Breed 0.24 0.24 0.10 0.10 0.17
(0002.46) (0001.37) (0.000.97) (0.00038) (0002.46)
Inte g 0.01 0.13 0.00 <001 0.05
(0.00025) (0001.10) (0.000.02) (0001.10)
La men ess 0.12 0.00 0.00 0.01 0.02
(0002.42) (0.000.04) (0002.42)
Mastitis 0.01 0.03 0.00 0.00 0.01
(0000.23) (0.000.45) (0.000.45)

 

" = Minimum and maximum values.

DISCUSSION

Cost, defined as a measure of an amount of value released in the acquisition or
creation Of economic resources in production (Hepp, 1985), is made up of two
components. One component is that cost measured in terms of money spent while the
other is the lost potential. Presently, NAHMS data can only be used to estimate dollars
spent
Qost eomputation'

The denominator of equation 3.2 represents the average number of animals at
risk of disease during a month. This is in contrast to most economic reports that
calculate the mean cost per case of disease. The cost per head figures reported in this
chapter represent the mean cost per case plus the mean risk of disease occurrence. This
figure is valuable as it conveys the expected probability of disease occurrence and the
expected cost from incident and prevalent cases.

e ts on var' s s ts test' atio

The drug and veterinary cost data sets were fairly accurate, since they were
substantiated (for the most part) by invoices from the producer’s veterinarian and/or
In the future, efforts should be made to differentiate between drugs

supplier.

administered under the supervision of a veterinarian and those administered strictly at

41

the discretion of the producer.

There were many omissions of these labor data by the producer. Efforts should
be directed toward educating the producers to record the time spent on various aspects
of their operations. The time spent performing a task should be recorded instead of
monetary figures, since labor wages fluctuate. The time spent then can be converted
into monetary terms using an accepted labor wage factor. The figures used for the
replacement value of an animal were those as given by the producer. These figures
were assumed to be fairly accurate since the producer would know the genetic potential
of the animal and current market price. It was difficult, however, to assess the accuracy
of these figures. An alternative way of collecting these data has been suggested, which
would involve collecting information about the animal and then using accepted
standards to estimate a replacement value for the animal in question. Another problem
associated with computing net cull cost was the fact that it was not possible to adjust
the net cull cost to include the probability that the animal would have been soon culled
regardless of her disease status. In other words, a cow may have had other problems
which when combined with disease, resulted in a culling decision. It may not be
reasonable to charge the entire cost of culling to disease X. Further reports should
focus on methods for addressing this issue.

The figures used for the value of dead calves were those given by the producer.
This can cause problems as seen in Table 3.2 for gastrointestinal disease in calves in
stratum four. For reasons mentioned under the cull and death data section, the use of
a standard value for deacon" calves has been suggested as an alternative. In these
results, the milk loss estimated was that discarded due to treatment. In some limited
instances, it also included milk production lost due to an acute disease. In such cases the
loss was the producer’s estimate of the difference between what the cow was producing
before and during the illness. These estimates of milk loss must be evaluated very

cautiously. First, all discarded milk should not be assumed to be a loss. This is because

 

4Deacon calves = Calves sold under seven days old

42

some milk is fed to calves, in which case some money (approximately $7.00 per cwt)’
would be saved in buying milk replacers. To correct for this discrepancy, the estimates
were adjusted to account for the discarded milk fed to calves. The producers reported
the percentage of discard milk fed to calves. Second, subclinical effects of disease on
milk production could not be estimated with data from the conventional NAHMS data
collection procedures where individual cow IDs are not available. Also, a decrease in
milk production will cause a decrease in feed intake with a corresponding decrease in
cost (savings) Further studies were conducted to improve these estimates in NAHMS,
and are reported in Chapter 8

It is felt that preventive cost figures were underestimated. There was great
difficulty in recording bulk purchases and it was not always possible for the Veterinary
Medical Officer (VMO) to know if individual doses of drugs recorded in the current
month might have been recorded as a bulk purchase in a previous month. Bulk
purchases may not have been recorded as the VMO was anticipating collection of those
costs at time of administration to the animal. Another problem in the preventive data
relates to which disease should be charged for a certain preventive measure. In case of
a multivalent vaccine against Infectious Bovine Rhinotracheitis, Bovine Viral Diarrhea,
and five strains of Leptospirosis, it was difficult to determine which disease was being
prevented. Thus, the cost to vaccinate against one of these diseases was estimated as the
total cost of the vaccine divided by the number of disease entities or the cost was
attributed to the syndrome the producer was concerned about preventing. The merit of
this approach may be questionable, and some standardized procedure should be agreed
upon.

e t es

Due to the grouping of disease problems used, the dollar values in this chapter

may not be directly compared to other reports in the literature, even if values from

those reports were to be adjusted to current monetary values. At this point, it is not

 

sPrice of reconstituted milk replacer based on a sample (n=4) of Michigan feed suppliers,
October 1987

43

possible to generalize the monetary figures reported and conclude that a given amount
of money could be saved on a given farm by preventing disease (X) This is true for 3
reasons: 1) some disease is unpreventable and this cost never can be recovered; 2) as
discussed, current cost estimations are incomplete and should be used with caution; 3)
whereas application of standards may improve cost estimations for extrapolation to a
reference population, use of standards or population estimates on a given farm may be
fraught with hazards (Lloyd, LIAI- 1987) The cost estimates reported here might be
called gross, short term costs of clinical disease. They are gross because revenue
increasing effects of disease, such as the savings in feed costs due to the animal being
off feed, were not included. It should also be noted that gross costs overestimate the
true net costs of disease. The costs are considered short term since the chronic and long
term effects of disease (e.g, those on reproductive efficiency) were not included. Even
though occasionally some registered cattle might have been overvalued, we feel that
many gross costs were underestimated or omitted. The costs reported in this chapter,
therefore, should be considered as the lower bound of the gross costs associated with
disease occurrence and prevention.
Seggestiens fer impzoving the eccezaey ei cos; esiimetes

Future efforts need to focus on methodologies for estimating costs associated
with lost potential due to diseases within the NAHMS program. To be able to estimate
costs of lost potential associated with disease, it is essential to have individual
identification of animals and the NAHMS program should strive to achieve such status.
Alternative methods for estimating the value of the animal, as opposed to accepting the
farmer’s figures, should be explored. More rigorous quantitative methods of estimating
costs associated with diseases, using data from an observational prospective study of

multiple dynamic populations, like the NAHMS, should be applied.

CHAPTER 4

The Application of simulation models and systems analysis in Epidemiology: A review

ABSTRACT

A method for classifying epidemiologic process models is presented along with
a brief history of epidemiologic modelling. Epidemiologic models are distinguished as
being associative or process models. Associative models attempt to establish etiology by
observing the associations of various risk factors with the occurrence of disease. Process
models attempt to quantitatively describe the course of disease in a dynamic population,
beginning with hypotheses about the underlying structural processes involved. A process
model can be further classified according to: 1) how it models the effect of chance, 2)
it’s application perspective, 3) the mathematical treatment of time, 4) the computational
treatment of individuals, and 5) the method for determining a solution.

The literature was reviewed for examples of applied epidemiologic process
models. Examples are cited and classified according to the proposed classification

method. Suggestions for further research are made.

INTRODUCTION

It has long been recognized that the occurrence of disease is a result of
interactions between components of the famous agent, host, environment complex. The
discipline of epidemiology has developed as a result of efforts to unravel the mysteries
of this complex. A survey of current epidemiologic literature (Susser, 1985) shows most
of the mathematical and quantitative work in epidemiology has resulted in what King
and Soskolne (1988) have termed associative models. These are models that attempt to
establish etiology by Observing the associations of various risk factors with the
occurrence of disease. This approach has been very fruitful and has resulted in a variety

of health recommendations, particularly with reference to individual risk factors for

44

45
chronic and noninfectious disease.

However, these associative models generally overlook the fact that interactions
in this famous complex are dynamic and relationships change over time, as do the
populations in which these interactions are occurring (Anderson and May, 1985;
Catalano and Serxner, 1987) Efforts to address this issue of dynamic interactions in
epidemiology have resulted in what are best termed process models (King and Soskolne,
1988) Process models attempt to quantitatively describe the course of disease in a
population, so that state of the population, in terms of number infected, susceptible, etc.
can be expressed over time. The goal of this paper is to focus on this latter type of
modelling. The objectives are: 1) to present a brief perspective on the development, past
and present, of epidemiologic process models, 2) to Offer a method for classification of
these process models, and 3) to classify specific applied models, with their application

in veterinary or human epidemiology.

HISTORY

It is interesting that some of the earliest epidemiologists were process modelers
(Susser, 1985) Early workers such as William Farr in 1840, Brownlee, Greenwood,
Kermack, and McKendrick, observed the consistent patterns of the occurrence of
epidemics and developed mathematical representations of these patterns with the hopes
of predicting the course of epidemics, Lpri_or_i. One of the first and few "successful"
attempts at modelling was on a veterinary problem. In a letter to the London Times
in 1865, W. Farr used an equation of second and third ratios to predict the outcome of
a rinderpest epidemic in England. This success was not often repeated but it encouraged
workers like Brownlee who persisted in the attempt to fit epidemic curves to variations
of the normal curve (Fine, 1979). Bailey (1975) mentions the work of Greenwood,
Kermack and McKendrick along with Hamer, Soper and Ross who developed versions
of what would later be called mass action models. Wade Hampton Frost, the first chair
of epidemiology at The Johns Hopkins School of Hygiene and Public Health, was the

originator of the Reed-Frost model of epidemics which still finds wide applicability

46
today (Abbey, 1952; Ackerman e; e1, 1984)

Given the illustrious beginnings of early process modelling, one might well ask,
why is this not an important part of epidemiology today? A further look at the history
of epidemiology and process modelling might offer some possible explanation. As the
early 20‘“ century progressed, epidemiology and process modelling were cooperative
partners in addressing disease control problems such as malaria and helminth infections
in humans, particularly schistosomiasis (Fine, et_al_., 1982; Hethcote and Yorke, 1984;
Anderson and May, 1985; Dietz and Schenzle, 1985) This assessment, of cooperative
partnership, is based on the observations from these reviews, and others (Bailey, 1982;
Koopman,1987), showing mathematical development concurrent with data collection and
disease control policy recommendations resulting from models. Nobel laureate, Sir
Ronald Ross, derived the first threshold theorem from a differential equation model
(Ross, 1911) This model determined that there was a threshold density of man and
mosquitoes below which malaria would not be able to maintain itself. George
MacDonald’s (1956) conclusions, that control of adult mosquitoes by residual insecticides
is more effective than larval control, is considered, by some, as "the single most
important insight into public health planning from modelling" (Dietz and Schenzle, 1985)
MacDonald (1965) also published an important paper on the dynamics of schistosome
infections and humans that has spawned a great deal of mathematical development in
parasitology, this is thoroughly discussed in Anderson and May (1985)

After this time, however, one can see a divergence between applied epidemiology
and mathematical modelling (Bailey, 1975, Thrusfield, 1986) Bailey (1975) suggests this
point of divergence occurred around 1957. Susser (1985) infers the change began after
World War 11. During this period it is possible to perceive two responsible forces. First,
epidemiologists are beginning to be more concerned with chronic, noninfectious diseases
(Susser, 1985; King and Soskolne, 1988), which tend to focus on individual risk factors
versus population dynamics, and find more use for associative (statistical) models than
for process models. Secondly, the limiting assumptions of the early mathematical

models, the mass action and chain binomial, began to impinge on their practical

47

applicability. These limiting assumptions will be discussed briefly later. As a result, the
models were not able to describe recurrent cycles of disease and fell out of use by many
epidemiologists (King and Soskolne, 1988)

The net result of these phenomenon can be expressed by the nursery rhyme
bemoaning the fact that "the dish (epidemiologist) ran away with the spoon" (statistician),
and left the cow (mathematician) to more esoteric pursuits, such as ”jumping over the
moon". This observation has been echoed by the mathematicians themselves (Bailey,
1982; Bart et a], 1983) One leader in the field of measles and helminth modelling has
noted: " some of the mathematical literature has taken on a life of its own, free from
data and full of elegant theorems in hopeful search of a disease" (May, 1982) The
modelling literature that occurs after this time is largely theoretical (Wickwire, 1977;
Mollison, 1977; Dietz and Schenzle, 1985; Isham, 1988) and difficult for the non-
mathematician (Koopman, 1987; King and Soskolne, 1988)

Unfortunately, a great deal of this rich theory has been overlooked by most
epidemiologists. This is particularly a handicap for the veterinary epidemiologist, who
in the majority of cases, is dealing with disease in dynamic populations. It may also be
a fair assumption that he or she is often dealing with infectious disease or parasitic
disease with which almost all of the process model development has dealt.

During this same post-war period, separate from epidemiology, the theory and
practice of systems analysis begins to develop (Chestnut, 1965) This methodology has
enjoyed a very fruitful tenure with a wide variety of applications to industrial
processing (Law and Kelton, 1982), management and social sciences (Sutherland, 1975),
ecology and entomology (Kitching, 1983) Before the late 1970’s only a few apparent
applications of this theory to epidemiology can be found (Waaler e; 111, 1962; Brogger,
1967; Waaler, 1968; ReVelle e1 e1, 1969) The count is increased if one includes the few
health care management applications (Farrow et §_l_, 1971; Bailey and Thompson, 1975)

In the late 1970’s and early 1980’s one can see signs that the once separated fields
of dynamic mathematics and epidemiology are beginning to reunite (Nokes and

Anderson, 1988) Epidemiology is bringing along the more fully developed field of

48
statistics, and dynamic mathematical disease models have been enhanced by computer
simulation. Simulation allows for relaxation of some of the assumptions, while
decreasing the need for rigorous mathematics and closed form analytical solutions. This
approach can more effectively deal with nonlinearities, time dependence and various
forms of feedback (Habtemariam e1; al, 1982b; Angulo, 1987) The possibility that systems
science will begin to contribute to epidemiology is suggested by Bailey (1982), Koopman
(1987), and some examples in the current literature which will be discussed below.
Koopman (1987) calls for a science of transmission systems analysis which merges the
mathematical theory of dynamic populations, with simulation modelling, as in Ackerman
e_t e1. (1984), with a constant eye to statistical interpretation of real world data, as in
Haber, Longini, and Cotsonis (1988) Stimulated by the current epidemic of human
immunodeficiency virus (HIV) infections and the call for more production and
economically oriented veterinary medicine, it is anticipated that this science of
transmission systems analysis, or the systems approach will gain an increased role in

epidemiology.

CLASSIFICATION

Any new methodology or discipline seems to suffer from an ambiguity of
terminology and lack of a unified classification scheme. This ambiguity seems to exist
in epidemiologic process modelling. The result is an increase in the amount of words
required to communicate the essential features of a model, miscommunication and an
overall decrease in the rate of new developments. Based on the writings of various
authors, a means of describing and hence classify current process models is presented
in this paper. It is hoped that all current models can be described in terms of these
various characteristics. Specific applied models published since 1970 are then
characterized along with their apparent application. An effort has been made to include
only papers that are considered to be applied and epidemiologic in nature. The
determination of the whether a paper is applied or theoretical is not always clear.

Applied papers are those that were deemed to be attempting to answer a specific

49

epidemiologic question, using data that is current enough to be considered useful. It is
not necessary that the data be collected primarily for the model, as most models depend
heavily on literature for estimates of many parameters. Some models were considered
theoretical, and excluded even though they employ current data. The reason being it was
perceived, by the authors, that the purpose of the data was only to evaluate behavior of
the model versus make disease control reccomendations. Epidemiologic papers are those
that relate to control of disease in animals or humans Agricultural production models
(Jenkins and Halter, 1963; Oltenacu 933], 1980 and 1981;) and statistical simulation models
(Lemeshow e1 31, 1985; Sutmoller, 1986: and Akhtar e_t e1, 1988), along with econometric
simulations (McCauley, gee], 1977) were generally excluded. No attempt has been made
to evaluate the usefulness or quality of the specific models included, or the validity of
their conclusions.

Secondly, three general types of models are identified and described. These
genera seem to represent most models that have been presented to date. Identification
of a model’s genera along with it’s specific classification will convey most of the

important information on a model’s technicalities.

ass' 'c io t

The classification of epidemiologic models might best be achieved by the
application of 6 characteristics that would express most of a model’s salient features
(Figure 4.1) These characteristics are: 1) the model’s causal perspective, 2) how it models
the effect of chance, 3) it’s application perspective, 4) the mathematical treatment of
time, 5) the computational treatment of individuals, and 6) the method for determining
a solution. Each of these characteristics are dichotomous, therefore for a given
characteristic a model will generally have one or the other traits. This allows for
flexibility in model characterization along with simplicity, since many types of models

can result from various combinations of these traits.

SCI

Characteristic Trait/Classifier
Stochastic, STDC

Effect of chance.::::::::
Deterministic, DETH

Structural (a priori)
Application .=::::::::::::
Perspective Functional (a posterior)

 

,5 Discrete time, DT (difference equations)
Process ‘ Mathematical ::::
(explanatory)\ Treatment of Time Continuous time, CT (differential
Causal /////// 4. equations)
Perspective ‘

i\

. Discrete entity, DE
Computational ‘,,,-”””

Treatment of
Individuals ‘~““~“‘~ Continuous entity, CE

  

Analytical, ANL
Method for

Determining “-~L‘e“_~‘
Solution Simulation, SIM

Associative
(emperical)

Figure 4.1 Proposed Classification Method for Process Epidemiologic Models

A model’s causal perspective reflects the nature of the original hypotheses that
an investigator may have been interested in. Associative models will infer causality
without a knowledge of the pathways or processes leading to the observed phenomenon.
Process models begin by defining hypothesized pathways and structural processes that
may describe the system under investigation. As already stated, this paper is confined
to process versus associative or statistical models. So our first characteristic is defined;
a model is either associative or process. This distinction of associative versus process
seems to be similar to Thrusfield’s (1986) designation of empirical versus explanatory
models.

Following King and Soskolne’s (1988) hierarchy, we can distinguish the
characteristic of how a model relates to the effects of chance. A model can be described

as being stochastic (STOC) or deterministic (DETM) Stochastic models include elements

51

of random variation and chance. Fully stochastic models, if run repeatedly will lead to
a distribution of epidemic sizes and durations (Ackerman et_ a1.) These fully stochastic
models are exhibiting the threshold theorem of epidemics (McKendrick, 1926) Other
stochastic models, of non-infectious disease will include the random effects of certain
variables, but will not exhibit the threshold phenomenon. Stochastic models have the
advantage of reflecting the realistic aspects of chance and uncertainty in a model’s
behavior. The predictions can be expressed with confidence intervals and expected
values instead of just point estimates. Deterministic models give the same result, every
time they are run, and one can consistently determine the state of the model for any
given set of initial starting values and parameters. Deterministic models are useful for
determining the sensitivity of a system’s behavior to changes in certain parameters.
The next level of classification is its application perspective. A model is either
functional or structural (King and Soskolne, 1988) . This is similar to Fine’s (1982)
distinction of descriptive (a posterios) versus :4 priori, or dynamic models. Structural
models attempt to portray the underlying mechanism of the disease transmission process
for the purpose of making em predictions or exploring implications of assumptions
and alternative assumptions. Most simulation models are of this type. On the other
hand, functional models begin from the standpoint of modelling a process, but their goal
is to quantitatively describe observed phenomenon, or to gain estimates of risk factors,
with a statistical application to the process model. Functional models attempt to model
a process and look backward in time, whereas structural models attempt to look forward
in time and make predictions about future states of a population. These functional
models are not the focus of this paper, but they represent a fascinating application of
the interface between process modelling and statistics. An interesting example of
functional modelling is a recent paper by Haber (Haber e: e1, 1988) where a
heterogenous population model was used to assess the effects of various individual risk
factors for influenza. The model used was previously developed by Longini and
Koopman (Longini et_ al, 1982, 1984b, 1988) These are applications of chain binomial

models in a functional manner (Poku, 1979) Functional models would also include the

52

so called catalytic models (Muench, 1959): In these models prevalence data are fitted to
differential equations to estimate the age specific force of infection in a population
(Sundaresan and Assaad, 1973; Goldacre, 1977; Schenzle e_t, a_l, 1979, Fine and Clarkson,
1982; Remme et al, 1984; Nokes et 11, 1986; McLean and Anderson, 1988) Box-Jenkins,
autoregressive integrated moving average (ARIMA), and other time series types of
analysis, might be classified as functional models (Angulo et 31., 1977; Choi and Thacker,
1981; Cliff and Haggett, 1982; Helfenstein, 1986; Catalano and Serxner, 1987) Markov
models have also been used as functional models (Schwabe e_t_ a_1., 1977; Leviton e_t e1,
1980) A simulation by Goodger eLeL (1988) might be classified as a functional model,
as simulation was used as tool for making statistical inferences about the difference in
milk production in Streptoeoeegs egaiaetiae infected cows that were treated versus not
treated.

The next characteristic of a model relates to its mathematical treatment of time.
A model will be discrete (DT) or continuous time (CT) Discrete time models divide
time into units of equal duration and employ the algebra of finite difference equations.
For example, the number of susceptibles at the next time period equals the number of
susceptibles at this time period minus the number of new cases (S,+1 = St - C,+1) (Fine,
1982). Continuous time models treat time as a continuous variable and use differential
equations to express instantaneous rates of change. For example, the rate of change of
new infections (ie. infection rate) might be a function of the number of susceptible (S),
cases (C) and some contact parameter (b,) (dC/dt = S‘C‘b) The number of cases at any
given point in time is just the integral of this rate (Bailey, 1975)

For the computational treatment of individuals a model can be classified as
discrete entity (DE) or continuous entity (CE) Discrete entity models will be defined
as models that track one individual at a time through the simulation model. This
individual is exposed to infectious individuals and any other experiences, such as calving,
death, etc. The behavior of the system is the sum of the behavior of each individual.
These types of models can get very complex, and this increases as the number of

individuals in a population increases. This complexity has the disadvantage of increased

53

computer and programmer time and decreased intuitive appeal (Ackerman et_ el, 1984)
Continuous state (entity) models treat the number of individuals in any state as a real
number, they can be computed in continuous or discrete time. Continuous entity models,
or macro models (Ackerman e_t e1, 1984) tend to deal with homogeneously mixing
populations. The homogeneous population assumption can be a disadvantage if one feels
that interactions are not the same for each individual in the population. The advantage
is that the size of the population being Simulated will not effect the speed of computer
processing for continuous entity models. It should be noted that if a model is
mathematically defined in continuous time, ie. with differential equations, then it will
a continuous entity model. However, the distinction blurs when a differntial equation
model is simulated on a digital computer, since time is discretized into very small units
for numerical integration (Law and Kelton, 1982)

In terms of how a model arrives at its solutions, one can classify a model as
analytical versus simulation (Fine, 1982) Analytical models depend on mathematical
manipulation alone to explore the relationships between variables, ie. they seek a closed
form solution to the state of the system at some equilibrium. There is an extremely
large number of these types of epidemic models which are largely the domain of the
mathematician (Bailey, 1982) The advantages are that, they can be rigorously evaluated
and stability criterion determined. The disadvantages are that much realism is often
assumed away in order to produce a more tractable model, and they are inaccessible to
the non-mathematician. Simulation models depend on numerical substitution, according
to model defined rules, to find the expected outcome of a mathematical formulation.
(Fine, 1982; Ackerman e; 31.) The example models presented below are mostly
simulation models.

In summary, 6 characteristics have been presented for classification of various
epidemiologic models (see Figure 4.1) For each of these characteristics two possible
traits exist: process versus associative, functional versus structural, stochastic versus
deterministic, discrete time versus continuous time, discrete entity versus continuous

entity, and analytical versus simulation.

54

od 8
When categorizing and classifying models, some authors have mentioned various
types of models such as the mass action, the Reed-Frost, Markov models, network
models, matrix models, systems models and others. It is useful if these various types
are grouped into three genera: mass action models, chain binomial, and systems models

(Table 4.1) Grouping the models in this manner conveys a sense of a model’s

assumptions'and view of the system it is attempting to describe.

Mass action models refer to the phenomenon that infection is the result of the
random and homogeneous mixing of infectious and susceptible individuals within a
population (Fine, 1982) They can be deterministic or stochastic (Bartlett, 1953), and they
can be discrete (Soper, 1929) or continuous time (Bailey, 1955) However mass action
models are always continuous entity. Some of the limiting assumptions of these type of

models are that they assume random and homogeneous mixing, and there is a linear
relationship between the incidence rate and the number of cases (eg. C,+1/St = Ct “ B)

This linear relationship makes it is possible to erroneously calculate more cases than

there are susceptible, in a small population. Also, the epidemiologic meaning of the

transmission coefficient ([3), for mass action models, is not quite clear (Fine, 1982)

In order to overcome these limiting assumptions the chain binomial models were
developed (Greenwood, 1946) In these models, new cases of disease occur in a series of
stages. The number of cases at any stage will have a binomial distribution depending
on the number of infectious and susceptible at the previous stage (Bailey, 1975) These
models are fully stochastic, discrete time and continuous entity. These models assume
the period of infectiousness is relatively short and of constant duration, there is a
constant probability of infection in each serial interval. (Fine, 1982)

There are at least four types of chain binomial models, the Greenwood type
(Greenwood, 1946), Reed-Frost, the Elveback type, and Markov models (Table 4.2)
Markov models or chains are sometimes used for simulations. These are mathematically
equivalent to chain binomial models with a finite state and discrete time parameter

(Dietz, 1967)

Genera

Chain binomial

 

 

 

Mass action

Systems models

 

 

55

Type or field of origin

Greenwood
Reed-Frost
Elveback

Markov

Discrete time (difference
equations)

Continuous time (differential
equations)

Network theory

Diffusion theory

Control theory

Infectious epidemiology
(chain binomial, mass action)

Gaming theory (eg. Monte Carlo)

Optimization and operation

Figure 4.2 Genera of Epidemiologic Process Models

56

A special case of the chain binomial is the Reed-Frost model where the expected
number of cases for the epidemic can be deterministically derived from the recursive
formula shown in equation 5.1 (Ackerman e_t_ e1, 1984) This model is discrete time, and
continuous entity. Mathematically it is deterministic but can be made stochastic with
computer simulation. It still suffers from the assumption of random mixing, and short,
constant length of infectious period.

Ct+1 = S ‘ (l-qct) . (51)

where: C = cases, S = susceptible

q = l-p, p = probability of effective contact

A discrete entity version of the Reed-Frost model resulted in what is often
referred to as the Elveback type of model (Ackerman e; 31, 1984) In this model one
individual at a time is processed through a simulation model and randomly infected,
with the probability of infection derived from the above equation. These models have
the advantage of allowing for heterogeneity of contact and different infection
probabilities for each individual. However, they soon become very complicated and
computer intensive.

There exists a third genera of models that are not derived from any particular
mathematical school of thought. These we might call systems models. These models
use whatever mathematical or simulation techniques are necessary to describe the
particular system of interest, i.e. whatever works. This may include differential
equations (Thrusfield, 1986), Leslie matrices (Kitching, 1983), Monte Carlo theory, and
network theory (Paton and Gettinby, 1983). Cohen (1977) calls them hybrid dynamic
models when referring to the schistosomiasis models of Nasell (1976a; 1976b) and others
(Nasell and Hirsch, 1973), which employ Markov laws along with differential equations.
A variety of optimization techniques can also be included (Carpenter. and Howitt, 1988)
The mass action models and chain binomial models may often be the essential building
blocks of the systems models, but modifications are made in order to move away from
many of the limiting assumptions, and in order to represent the complexities of the

whole system.

57
The definition of systems analysis or the systems approach may seem to be as
broad as the problems it attempts to solve. However, certain consistencies in the various
definitions can be found. The essential features are that it 1) is a methodology for
solving unstructured problems 2) that begins with a defined set of needs, 3) moves to a
description of the whole system as it currently exists, 4) generates alternatives for

meeting the expressed needs, 5) evaluates those alternatives with various modelling

techniques, and 6) designs and 7) implements the policies found most capable of meeting
the needs (Checkland, 1981:161-191; Manetsch and Park, 1982:8-15) The two important
attributes are that it "overtly seeks to include all factors which are important in arriving
at a "good" solution, and it makes use of quantitative models and Often computer
simulation in making rational decisions.” (Manetsch and Park, 19828) Simply put, it is
a holistic approach (Martin e; a], 1987) Systems models offer the greatest potential for
future use as they are not limited by the assumptions of basic infectious disease models
(Bailey, 1982; Koopman, 1987) They are also very valuable tools for consideration of the
economics of disease and disease control.

It is possible, in ,m‘Ost cases, to apply the 6 classification criterion to systems
model and thus aid in giving a better description of these systems models. This is
important since these models do not easily fit into clear classes. An advantage of the
proposed classification scheme is its ability to describe the wide range of models in

existance. For example, models that use queuing theory might be described as discrete

time, discrete entity, stochastic simulation models (Law and Kelton, 1982)

'O 0 lie (1
Shown in Table 4.2 is a listing of those publications that were chosen as applied
epidemiologic models published since 1970. The table shows only models of the
structural process type. The other important characteristics, for each model, are

indicated, as well as its general type.

58
Of the over 200 simulation and mathematical articles reviewed for this paper,
only 49 were considered as applied, epidemiologic, structural, process models. Of those,
19 seemed to represent enough complexity and holistic view to be classified as systems
models. It is interesting that the majority of the systems type models dealt with
veterinary or zoonotic disease problems. This reflects the importance that this approach

has for veterinary epidemiology.

59

Table 4.2 Classification of applied epidemiologic structural process models

 

Reference Application

Chance Time

Entity Method Genera

 

Barret, 1988 hetersex spread of HIV in

early epidemics
Carpenter and Howitt, 1988 determine optimal downtime
and head placement for a,
broiler operation

evaluate economics of
alternatives to vaccination
for control of FMD

Di jkhuizen, 1988

Oluokun and David West, 1988 evaluate factors controlling
CALF MORTALITY in
Nigeria, with economic effects
Sorensen, 1988 evaluate economic effects of
PNEUMONIA levels in a

dairy cattle herd

examine alternatives for
prevention of TUBERCU-
LOSIS with isoniazid

Tse vat, e5 s_l., 1988

STOC

STOC

DETM

DETM

STOC

DETM

DT

CT

DT

DT

DT

DT

DE

DE

CE

DE

DE

DE

SIM

SIM

SIM

SIM

SIM

SIM

C.B.

SAM

Markov

SAM

SAM

Markov

 

Anderson, 5; e1, 1987 evaluate impact of mass vacc.

on incidences of MUMPS

economics of control of
BRUCELLA OVIS

Carpenter, e; 31., 1987

Snaiyze spread of
- HEPATITIS A in day care
centers

Sattenspiel, 1987

DETM

DETM

STOC

DT

DT

CE

DE

SIM

SIM

SIM

Elve.

 

Anderson and May, 1986 find important factors
for future rends in the
HIV epidemic
Anderson and Greenfell, 1986 impact of vaccination

- strategy on CONGENITAL
RUBELLA SYNDROME (CR8)

Dijkhuizen, e; s1, 1%6 economics of culling and

Papoz, es 91., 1986 predict rates of sero-
conversion to TOXOPLAS-
MOSIS in a population
Shonkwiler and Thompson, 1986 study outbreak of
TOXOPLASMOSIS

DETM

DETM

STOC

DT
DT

DT

CE

CE

DE
CE

DE

SIM

SIM

SIM
SIM

SIM

MA.

MA.

SAM
C.B.

SAM

 

Paton and Gittinby, 1985 evaluate control strategies

for QSIEBIAQIA in sheep
Longini, et el, 1985 predict global spread of
HONG KONG INFLUENZA

DETM

DETM

DT

CE

CE

SIM

SIM

SAM

SAM

 

Table 4.2 (cont)

Aekermamfifl..1984

Levy, 1984

many applied and theoret-
ical models of FOLIO and
INFLUENZA

determine the effect of
MEASLES vaccination
program on number of
susceptibles

DETM

DE,CE

CE

SIM

ANL

 

Anderson and May, 1%3

Hethcote, 1983

Smith, 1983

Habtemariam and Cho, 1983

Paton and Gettinby, 1983

examine impact of different
vaccination policies on

incidence of MEASLES and CR8

cost-benefit analysis of
vaccination strategies for
MEASLES and CR8

evaluate alternative control

“mesh. for BABESIA m

determine level of POULTRY
INSPECTION for any given
farm at slaughter house

control of OSTERTAGIA in
sheep

DETM

DETM

DETM

DETM

DT

DT

DT

CE

CE

CE

CE

ANL

ANL

SIM

SIM

ANL

M.A.

M.A.

SAM ‘

SAM

SAM

 

Croll, e; 11., 1982
Cvjetanovic, e; 31., 1982

Habtemariam, e; 31., 1982a

Habtemariam,e_§ g1, 1982b
Habtemariam, g; 51. 1982c

Hethcote, e; 31., 1982

effectiveness of mass treat-
ment for eradication of

WW

. cost effectiveness analysis

of vaccination programs,
MEASLE and POLIO in USA

benefit-cost analysis for

control of TRYPANOSOMIASIS

describe epidemic and
endemic characteristics
of TRYPANOSOMIASIS

evaluate disease and vector
control strate of
TRYPAN MIASIS

evaluate 6 prevention

methods GONORRHEA control

DETM

DETM

DETM

STOC

STOC

DETM

DT

CE

CE

CE

CE

CE

CE

SIM

SIM

SIM

SIM

SIM

ANL

Matrix '

Matrix

SAM

SAM

M.A.

 

Dietz, 1%1

Kramer and Reynolds, 1981

Meek and Morris, 1981

determine best method to ~
compute cost for vaccina-
tion strategies of MEASLES
control

evaluate 28 control
programs for GONORRHEA

evaluate control ograms
for OVINE FA IOLIASIS

DETM

STOC

STOC

DT

DT

CE

DE

DE

ANL

SIM

SIM

M.A.

SAM

SAM

 

Carpenter and Riemann, 1980

BIC for eradication of .

Mmslssms

DETM

DT

CE

SIM

Markov

Table 4.2 (cont)

magma

Knox, 1980

MacDonald and Bacon, 1980

61

' identify environmental

variables important in the
prevalence of HYDATTD
DISEASE

predict effectiveness of
alternative vaccination
policies for CRS

explore effect of vaccination
of foxes for RABIES control

DETM

DETM

DETM

DT

CE

CE

SIM

SIM

SIM

SAM

SAM

 

Longini,;ieLI978

Nasell, 1977

Elveback, £3 3.1-I 1976

Hugh-Jones, 1976

Miller, 1976

Roe and Morris, 1976

optimum INFLUENZA vaccine
distribution among age groups

test efficiency of sanitation for
control of SCHISTOSOMIASIS

effect of vaccination for

INFLUENZA A in school children

test effect of milk-lorry
borne spread of FMD

simulate spread of FMD
across the USA

BRUCELLOSIS control in
Australia

DETM

DETM

STOC

STOC

DETM

STOC

DT

DT

DT

DT

CE

CE

DE

DE

CE

DE

ANL

ANL

SIM

SIM

SIM

SIM

M.A.

Elve

SAM

Markov

Elve

 

Horwitz and Montgomery, 1974

Reynolds and Chan, 1974

Dietz, £1 91- 1974

Cvjetanovic e1 g1, 1973
Cvjetanovic, g 11., 1972
Cvjetanovic, 3 a1, 1971

Elveback, g :1. 1971

‘effect of underreporting

on alternative vaccination
programs for MEASLES in USA

evaluate control programs
for GONORRHEA

quantitate different inter-
ventions for MALARIA control

BIC analysis of sanitation
versus vaccination for
CHOLERA

BIC analysis of different
vaccination programs for
TETANUS

BIC analysis of sanitation
and mass vaccination for
TYPHOID FEVER

effect of school closing and
vaccination on spread of polio

DETM

DETM

DETM

DETM

DETM

DETM

STOC

DT

DT

DT

DT

DT

CE

CE

CE

CE

CE

DE

SIM

SIM

SIM

SIM

SIM

SIM

SIM

M.A.

E

E

Elve.

 

? :- not enough information to classify

M.A. - mass action
C.B. - chain binomial

Rf. - Reed-Frost
SAM - systems model

- Monte Carlo, chain binomial

Elve. - Elveback type of chain binomial

FMD - foot and mouth disease

BIC - benefit-cost analysis

- human immunodeficiency virus

- congenital rubella syndrome

62
DISCUSSION

It is possible that some models considered not to be systems models should have
been classified as such. These could be considered as systems models of a very narrow
well defined system. For example Carpenter, e_t e1. (1987), is a Reed-Frost model where
the system might be defined as only the sheep in the simulated herd with the only
inputs from the environment being vaccination and price information. As one can see,
the differentiation of systems models from the other model types is somewhat
debatable. It is however, still a useful distinction. This is particularly true if one
considers the historical perspective from which the system modelling approach is
derived, as opposed to the mass action and chain binomial models. These latter types
of models are derived from models of the dynamics of interactions between individuals,
with strict emphasis on the assumptions of infectious disease. By collecting the
experiences of individuals they are able to describe a dynamic population. The systems
models, on the other hand, begin from the top down in describing the behavior of an
unstructured problem. A systems model will use any mathematical, computerized or
symbolic means in order ‘to describe the important phenomenon. If a systems model
ends up using a mass action or chain binomial model, it is because it is thought to best
represent the behavior of that system, although modifications are usually made to reduce
the assumptions required. It is not being suggested that systems models have no
assumptions, or that they will accurately predict reality. However, if assumptions are
made it is because they are not considered to be important, or, lamentably, because the
data are lacking. This is in contrast to the other model types which often make
assumptions due to mathematical constraints of the base model.

In reference to whether a model should be considered as applied or theoretical
the distinction was usually clear. Many articles concluded by saying that the model
could be applied to a specific problem, implying that it had not been applied as yet.
Some models were obviously theoretical, as they began with another author’s model and
made certain changes, testing the effects of those changes against an example dataset.

There is a much smaller group of articles that seemed to have originated with the intent

63
of making some epidemiologic conclusions, however, due to lack of data, the authors
were forced to conclude that the models could be more valuable, given the appropriate
data. It is unfortunate that a great deal of excellent work was excluded with these
criteria.
Eexther seseaich

It is often the case that the modelling exercise brings to light important
deficiencies in the available body of knowledge (Martin e_t_ e1, 1986) The model can be
used to demonstrate the importance of the missing data and direct data collection
efforts. Model building is an important means of generating and formalizing
hypotheses. For this reason, preliminary work in population dynamics and dynamical
disease control should begin with model building. This is in contrast to most
experimental research that begins with a hypothesis and small data collection efforts
(pilot studies), followed by larger efforts ending with analytical model building. A pilot
study in population epidemiology should involve model building and testing.

There is need for mOre data collection efforts generated by systems modelling.
Besides the above noted‘w‘Ork that was excluded, by lack of data, some of the work cited
in table 4.2, was lacking data in some areas. As a result, assumptions were often
necessary, and parameter estimates were often extracted from the literature. Even
when parameter estimates are available, from current data, they are often assumed to
remain constant throughout the simulation period, and are not changed in response to
changes in the system being modelled. Another weakness of many parameter estimates
has been discussed by Lloyd, eLe], (1987) This relates to that fact that standards are
often used when making decision for a specific situation to which the standards may not
apply. Modelling techniques to overcome these shortcomings and develop models that
will adjust to specific application are being developed (Lloyd, 1989)

Given the value of systems modelling and the relative paucity of work in this
area it is reasonable to conclude that a great deal more work needs to be done in terms
of model development and application of current modelling types to specific veterinary

problems (Riemann, 1988) It is likely that veterinary epidemiologists should be the

64
leaders in this area as they commonly deal with populations and the unit of concern is
often the herd versus the individual. It is also notable that much of the work is related
to the behavior of these populations within the context of the overall production system.
Here one can see the need for the systems view of the interactions between the
financial system, animal system, and, say, the crop production system. The systems
approach is more than a modelling technique, it is a point of view that is essential for
the modern practitioner of veterinary preventive medicine, and its development should
be encouraged. It is also reccomended in the educational curriculum of medical and

public health practitioners (Nokes and Anderson, 1988)

CHAPTER 5

Risk factors associated with clinical respiratory disease in Michigan dairy cattle:

Analysis of data from the National Animal Health Monitoring System

ABSTRACT
Data from round I of the National Animal Health Monitoring System in

Michigan were analyzed with the objective of identification and estimation of

the relative importance of various risk factors for clinical respiratory disease in 3 age
groups of dairy cattle. A stratified random sample of 60 dairy herds was obtained.
Herds were visited monthly to collect data on the incidence of various diseases including
clinical respiratory disease. A management survey was completed at the end of the 12
month follow-up period. A general linear regression model was employed to determine
variables associated with the incidence density of respiratory disease. A conditional
logistic regression was used to estimate odds ratios, with adjustment for confounding and
herd size effect. In calves the odds ratio for being born in a multi-animal maternity
area was 10.6. Having said for bedding in the maternity area gave an odds ratio of 2.8
and receiving colostrum through a tube feeding versus nursing resulted in an odds ratio
of 1.45. Housing type had no effect in calves. In young stock, which are animals from
weaning to first parturition, receiving hay that had been stored outside with no
protection slightly increased the risk of disease. In cows the risk of disease was 18 times
greater if more than 50% of the non-milking, non-field work labor was performed by

hired personnel. For cows living in loose housing the risk was decreased.

INTRODUCTION

Respiratory disease plays a significant role in mortality and morbidity
experiences of the United States dairy cattle farm (Martin and Wiggins, 1973, Oxender
mi. 1973; Curtis 9131, 1988a) Most work has focused on disease in calves less than 6

months of age, yet disease in older heifers and adults may still be important. For

65

66

example, in the 12 month period of June 1986-July 1987, the National Animal Health
Monitoring System in Michigan estimated that approximately 32,000 out of 690,000 young
stock, and 9,000 out of 345,000 cows were reported to have some form of respiratory
disease or pneumonia (see Chapter 1) A plethora of experimental research data exists
on the important factors affecting the physiology of this disease syndrome (Roy, 1979,
Yates, 1982; Roth, 1983), and some data exist from cross-sectional study designs. However,
only a few prospective, or longitudinal studies of northern dairy states have been
conducted (Curtis e131, 19883) The advantages and disadvantages of these differing
study designs have been discussed elsewhere (Dohoo and Waltner-Toews, 1985;
Waltner-Toews egg, 1986a)

Evidence from past research has implicated a set of risk factors for respiratory
disease which might be classified into 5 general categories, 1) macro-environmental, 2)
micro-environmental, or housing related, 3) nutritional, 4) immunological, and 5)
management or people related. Macro-environmental factors include season of the year,
local weather, and extremes'of temperature and humidity. Season is generally thought
to effect the incidence of"respiratory disease (Martin e_t_el, 1975b; MacVean e131, 1986;
Waltner-Toews et_e_1., 1986a; Waltner-Toews e;_a_1, 1986b; Curtis et__a_l, 1988b; and others)
The specific components of season that cause this effect are still in debate (Yorke MI.
1979) Much of the prior experimental work has been directed at determining the effects
of factors such as environmental extremes of temperature and humidity (Elazhary and
Derbyshire, 1979, Roy, 1979, Webster, 1981; Collier et_e1, 1982; Robinson e_Lal, 1983; Jones
and WebSter, 1984; Dennis, 1986; MacVean e_t_a_r_l., 1986; Jones 1987) In addition, MacVean
e_Lei. (1986) measured the effect of dust levels on respiratory disease incidence. Seasonal
effects are important from an epidemiologic standpoint as possible confounding
variables which are associated with the occurrence of disease and the hypothesized risk
factors (Rothman, 1986) However, it is reported that the specific effects of weather are
difficult to quantify due to the differences in housing effects and the ability of animals
to acclimate (Miller e_t_a_l., 1980)

Experimental studies tend to find housing patterns (micro-environmental) that

67

reduce weather extremes are generally beneficial (Roy,1979, Collier eLai, 1982; Roe, 1982;
Dennis, 1986) Yet the Observational evidence is inconsistent as to the positive effects
of these housing practices (Hartman e_Lei, 1974; Jenny et_a_l., 1981; Simensen, 1982;
Waltner-Toews eiel, 1986c; Curtis et_a_l., 1988b) For example, Waltner-Toews egi. (1986c)
showed that hutches reduced the risk of disease in calves by 25 times compared to those
housed inside in individual pens, while Curtis et_ai. (1988b) found that, in the summer,
calves housed in hutches had an increased risk of respiratory disease compared to those
indoors in group pens.

Micro-environmental risk factors related to the mixing of animals have been
implicated. These practices include crowding, and housing of susceptible animals with
infected (Waltner-Toews e_t_ei., 1986c); although this risk producing effect of the latter
is not consistently observed (Hartman et_ei, 1974; Simensen, 1982) The importance of
ventilation has been investigated, with various results (Mihajlovic et al, 1972; Donaldson,
1978; Pritchard etil, 1981), as has the effect of bedding type (Martin et_ai, 1980, Simensen,
1982; Curtis et_ei, 1988b) _. ‘. '

 

Of the important ‘nutritional factors, colostrum intake has received the most
attention (Gay, 1983) The amount fed and the postpartum time to feeding have been
found to be significant (Jenny 9131-, 1981; Mechor £1.11» 1987) The most beneficial route
of administration is still debatable (Withers, 1952; Speicher and Hepp, 1973; Ferris and
Thomas, 1974; Waltner-Toews mi, 1986c; Curtis et_r_ri., 1988b) The risk of using milk
replacer versus whole milk for- calf feeding has received mixed reviews (Oxender et_ai,
1973; Hartman 91.81- 1974; Jenny M1, 1981; Simensen, 1982; Waltner-Toews 9111., 1986c)
Selenium deficiency was shown to have no effect experimentally (Phillippo mi, 1987),
but some effect in observational studies (Waltner-Toews et_a_l_, 1986c)

Nutritional factors which affect older cattle have been evaluated in beef feedlots.

In the feedlot studies, high levels of grain feeding (Wilson et al,. 1985), and high and

 

early amounts of corn silage feeding (Martin et el, 1980; Martin et al, 1981; Hutchings
and Martin, 1983) increase disease and mortality rates. '

The effects of many of the aforementioned risk factors have been hypothesized

68

to have their effect through immunologic pathways (Roth, 1983) Other factors, such as
vaccination, are directly implicated in reducing disease rates or, in some cases, increasing
rates (Martin et_si, 1980; Martin eLai, 1981; Martin, 1983) Some viral pathogens have
shown evidence of reducing immune responses (Roth, 1983; Wilke, 1983; Baker 23.81» 1986;
Brown, 1988) These phenomena have not been carefully assessed in field studies of
dairy cattle populations.

Management, or people factors, represent effects of uncertain origin that are measured
by proxy variables, such as years of dairy experience (Hird and Robinson, 1982), herd
size (Martin et_s_i, 1975a; Jenny et_ei, 1981), or person responsible for feeding calves
(Speicher and Hepp, 1973; Simensen, 1982) The causal relationship of these variables to
increased risk of respiratory disease is not clear.

The risk factors identified are hypothesized to represent biologically plausible pathways
to disease. It is likely that important variables for the dairymen are those that are
tangible and economically feasible to alter. Field studies that measure the effects of
such factors in real world situations using statistical designs that allow for generalization
to other "average" farms‘in the northern United States should be beneficial. The
objective of this paper is to identify and estimate the relative importance of various risk
factors for clinical. respiratory disease in 3 age groups of dairy cattle using data collected

through the National Animal Health Monitoring System in Michigan.

MATERIALS AND METHODS
HQId sele‘etion eiid daze eeilectioii

As part of the National Animal Health Monitoring System in Michigan round
I (1986/87), a random selection of all Michigan dairy herds was obtained for one year
of follow-up. A detailed account of the selection of these herds, data collection tools,
and the data collected is presented in Chapter 1.

The producer was responsible for most of the diagnoses of respiratory disease,
although occasionally the diagnosis was confirmed by the local practitioner or rarely

by a diagnostic laboratory. The definition of disease for this study includes cases of

69
pneumonia and respiratory diseases not otherwise specified.

At the end of the follow-up period an extensive management survey was
conducted by a visiting veterinary medical officer (VMO) For many of the questions,
the producers were allowed to provide more than one response, since it was likely that
more than one type of management practice or housing system might exist on the same
farm.

Staiisiical analysis

Two types of statistical models were employed. A general linear model (GLM)
(SAS, 1985: GLM procedure, p. 433) was used where the dependent variable was the
annual incidence density (ID) of respiratory disease. Secondly, a conditional logistic
regression model (PHGLM, Harrell 1986) was used to estimate odds ratios for important
variables determined from the general linear regression model. The odds ratio measures
the strength of association between a factor and disease, or the probability of disease
given a certain risk factor. For the logistic model the annual incidence density was

dichotomized, for each ofth’e 3 different age groups, according to table 5.1.

‘

Table 5.1 Dichotomization of dependent variable (ID) for use in the conditional logistic
regression, by age group.

 

Age group tested in

 

 

Dependent
variable
name ‘ Meaning Calves Young stock Cows
DPOS3 ' annual incidence density (ID)
3 3 per 100 animal years
DPOS4 annual incidence density (ID) +
Z 4 per 100 animal years
DPOS.1 annual incidence density (ID) + +
_>_ 0.1 per 100 animal years
DPOS.2 annual incidence density (ID) + +

Z 02 per 100 animal years

 

70

The model building process was a manual form of the stepwise backward
elimination procedure. All variables were originally entered into the model. Variables
with a high p value, (P > 05) with the F-test were considered for deletion. If the
variable was not expected to be an important confounder, it was deleted. The model was
then recalculated If the p values of the reestimated model differed greatly from the
previous model, then the most recently deleted variable was incorporated back to the
model. The goal was a model with the fewest number of important variables, resulting
in more precise estimates for the remaining variables (Kleinbaum mi, 1982)

The odds ratios of significant variables, from the GLM, were then estimated with
a conditional logistic regression model. The conditional estimates were implemented by
application of a unique approach to the SAS proportional hazards model for survival
analysis (Harrell, 1986) It was thought that this approach was more appropriate given
the small sample size and large number of variables being tested (Kleinbaum e_t_a_i., 1982)
The herds were "matched" for herd size stratum, so the results are adjusted for the effect
of herd size. Conditional models contained only 2-3 variables; the variable of interest
and one or two confoun‘ders. The confounders represented non-mutually exclusive
responsive to questions that could be classified as one effect. For example, a herd could
have calf hutches (HUTCHCAF) and calves in the cow barn (COWBNCAF) The odds
ratios estimated for HUTCHCAF would adjust for the fact that the other category

(COWBNCAF) may have also been checked on the management survey.

RESULTS

The overall mean unweighted annual incidence densities of respiratory disease
for calves, young stock and cows was 3.12, _.467, and .19 cases per 100 animal years,
respectively. For calves the number of herds coded as DPOS3 (disease positive at ID >=
3 per 100) and DPOS4 (disease positive at ID >= 4 per 100) are 17 and 11 respectively.
For young stock the number of herds coded as DPOS.1 (disease positive at ID >= 0.1 per
100) and DPOS.2 (disease positive at ID >= 0.2 per 100) were 18 and 10, respectively; for
cows the numbers were 19 and 10 for DPOS.1 and DPOS.2.

71
The variables originally tested in the GLM models are shown in Tables 5.2 and
5.3. The frequency of positive responses to categorical variables and means for

continuous variables are also shown in these tables.

72

Table 5.2 Variables tested in general linear model (GLM) for effect on the annual
incidence density of respiratory disease in COWS and YOUNGSTOCK

(number of positive responses, or mean)

 

 

 

 

 

Age grp. testeg in
Variable Young
name Meaning of the variable Cows stock
STRAT‘ herd size stratum, 1 = 1049 cows(17) + +
2 = 5099(19), 3 = 100199(8), 4 = _>_ 200(4)
DAIRYEXP total years of dairy experience of + +
primary herdsman(27.4)
FARMPLAN‘ plans for the farm in the next year, + +
1 = expand(9), 2 = stay same(33),
3 = decrease size(1), 4 = sell(1),
5 = other ownership transfer(4)
MHIREPOS’ > 50% of milking is done by hired non- + +
family labor (n = 9)
OHIREPOS‘ _>_ 50% of non-field work is done by hired + +
labor (n = 11)
CAVFAC" type of calving facilities, 1 == multi 4-
animal maternity pen - MULTMATN
only(22), 2 = individual calving
pens.== INDVSTAL only(19), 3 = both
MULTMAIN and IN DVSTAL(3), 4 =
neither = calving with dry or
lactating cows(4)
HAYSTOROUT‘ hay stored outside uncovered (n = 13) + +
HSTORIN‘ hay stored inside (11 = 37) + +
HAYSTORCOV“ hay stored outside but covered (11 = 2) + +
HAYPROP proportion of total forage fed on that +
. farm that is dry hay (24%)
HLPROP proportion of total forage that is +
haylage (42%)
SCPROP proportion of total forage that is corn +
silage (33%)
STANCHCHL‘ cows housed in stanchions(2) +
STANCHYS young stock housed in stanchions(8) +
LOOSECL“ cows housed in loose housing(9) +
LOOSEYS“ young stock housed in loose housing(22) +
FSTALLCL‘ cows housed in freestalls(25) +
FSTALLYS" young stock housed in freestalls(9) +

 

"Class variables.

73

Table 5.3 Variables tested in {general linear model (GLM) for effects on the annual

incidence density 0

respiratory disease in CALVES (number of positive

responses, 01' means)

 

 

 

 

 

Variable Meaning of the variable

STRAT“ herd size stratum, 1 = 10-49 cows(17), 2 = 5099(19), 3 = 100199(8),
4 = 2 200(4)

DAIRYEXP total years of dairy experience of primary herdsman(27.4)

FARMPLAN’ plans for the farm in the next year, 1 = expand(9), 2 = stay
same(33), 3= decrease size(1), 4 = sell(1), 5 = other ownership
transfer(4)

MHIREPOS‘ _>_ 50% of the milking is done by hired non-family labor (n = 9)

OHIREPOS“ Z of non-milking, non-field work is done by hired labor (n = 11)

CAVFAC‘ type of calving facilities, 1 = multianimal maternity
MULTIMATN(22), 2 = individual calving pens INDVSTAL(19)
3 = both MULTMATN and INDVSTAL(3), 4 =neither calving
with dry or lactating cows(4)

BEFCAV’ cow stays in maternity area _>_ 3 days before calving (n = 16)

DISINF‘ use of disinfectants to wash maternity area, for those that do
wash the maternity area at least once per year (n = 13)

STRAWBED“ uSe of straw for bedding in maternity area (11 = 40)

SANDBED“ use of sand for bedding in maternity area (11 == 2)

CORNBED" use of corn fodder for bedding in maternity area (n = 2)

SAWBED‘ use of sawdust for bedding in maternity area (n = 13)

COLSBOTL‘ first feeding of colostrum delivered by bottle feeding (n = 40)

COLSTUBE‘I first feeding of colostrum delivered by tube feeding (n = 3)

COLSNURS“ first feeding of colostrum delivered by nursing darn (n = 23)

MILKREPL‘ fre uency of use of milk replacers versus whole milk 1 = < 10%

ft e time(16), 2 = 10=25%(1), 3= 25-50(6), 4= 5075%(4), 5= >

75%(19)

HUTCHCAF“ calves housed in individual hutches (n = 14)

COWBNCAF‘ calves housed in same barn as cows (11 = 17)

CAFBNCAF“ calves housed together in separate barn for calves only (n = 26)

 

*Class variables.

”Variable dropped from model to prevent singularity with remaining variables.

74
The variables in the final GLM model Odds ratios for selected variables, are
shown in Tables 5.4— 5.6. For those variables with estimated Odds ratios, the variables
that were included in the conditional logistic model are shown with their associated beta
values and standard errors. These are shown so that an Odds ratio could be estimated
for a herd that was positive for the variable of interest as well as one of the

confounders.

75

Table 5.4 Variables in the final GLM model for respiratory disease in CALVES.
Conditional odd ratios for interesting variables, adjusted for herd size strata.

 

Confounding vari-

 

F valve ables used when
Variables (df) Pr>F Odds Ratio (CI‘) estimating OR”
STRAT 1.65 (3) .198 NE"
OHIREPOS .34 (1) 565 2.8 (86, 9.0) MHIREPOS (B = ‘09,
SE = .88)
CAVF AC 6.32 (3) .002
MULTMATN .18 (1) .67 10.6 (1.98, 528) IN DVSTAL (B = 1.04,
only” SE = .855
INDVSTAL 9.44 (1) .0044 2.8 (.70, 11.6)
only"
BEFCAV 1.02 (1) 320 .32 (.09, 1.09) MULTMATN (B = 3.0,
SE = 1.2), INDVSTAL
(B = 1.28, SE = .96)
HUTCHCAF 2.23 (1) ‘ .145 185 (.61, 5.6) COWBNCAF (B = ’54,
. ' SE = .98
COWBNCAF 2.53 (1) .1217 58 (.12, 2.9) HUTCHCAF (B = 0.6,
SE = .67)
SAN DBED 1677 (1) .0003 2.8 (.49, 17.1) none included
CORNBED .03 (1) ' 871 NE
SAWBED ‘ 52 (1) .472 NE
DISIN F . 4.73 (1) .037 .37 (.063, 2.15) none included
COLSBOTL .6 (1) .44 N E
COLSTUBE 558 (1) .0247 COLSBOTL

145 (30, 7.0)

(p = .46, SE = 1.08)

 

" 90% confidence interval.

"“ NE = not estimated.
“" the effect of that variable is contrasted against all others in the CAVFAC effect.

m shown with associated coefficients (B) and standard errors (SE)

76

Table 55 Variables in the final GLM model for respiratory disease in YOUNG
STOCK. Conditional odd ratios for interesting variables, adjusted for herd

size strata.

 

Confounding vari-

 

F valve ables used when
Variables (df) Pr>F Odds Ratio (CI‘) estimating OR‘”
STRAT 83(3) .48 NE"
HSTORIN 2.08 (1) .16 NE
HSTOROUT 353 (1) .07 152 (50, 4.6) HSTORIN (a = :12,
SE = .71)
HSTORCOV 192 (1) .17 NE
HLONLY 2.38 (1) .13 NE
STANCHYS .40 (1) 52 NE
LOOSEYS 1.84 (1) .18 .79 (25,24) STANCH ((3 = 32,
SE = .84),
FSTALL (p = '32,
SE = 86)
FSTALLYS .91 (1)7 34
OHIREPOS 111 (1) 29

 

"‘ 90% confidence interval.
*" NE = not estimated.

“" with associated betas (B) and standard errors (SE)

77

Table 5.6. Variables in the final GLM model for respiratory disease in COWS.
Odds ratios for interesting variables, adjusted for herd size strata.

 

Confounding vari-

 

 

 

F valve ables used when

Variables (df) Pr>F Odds Ratio (CI‘) estimating OR“

STRAT .94 (3) .43 NE‘

CAVFAC 3.75 (3) .02

MULTMATN" .94 (1) .34 1.7 (.39, 7.3) INDVSTAL (B = 1.45,
SE = .97)

INDVSTAL” .94 (1) .34 43 (86, 21.18 MULTMATN (B = 53,
SE = 88)

STANCH 1.98 (1) .17 2.9 (83, 103) none included

LOOSE 2.92 (1) .09 .87 (.22, 3.4) none included

FSTALL .02 (1) .90 NE none included

CSfitOP 264 (1) 11 NE

OHIREPOS 6.61 (1). .014 18 (.47, 1.9 MHIREPOS (B = 103,
SE = 1.18)

MHIREPOS 1.62 (1) .21 NE

DAIRYEXP 157 (1) 22 NE

 

" 90% confidence interval.
“‘ NE = not estimated. ‘
"" the effect of that variable is contrasted against all others in the CAVFAC effect.

“" with'associated coefficients (B) and standard errors (SE)

DISCUSSION

It is difficult to compare the reported disease frequencies in this paper with
previous reports as they represent a mean rate which may not be the best measure of
central tendency for a skewed distribution (Curtis et_ai. 1988a) Also it is difficult to
compare frequencies if they are computed in different manners. For example,
Waltner-Toews et_ei., (1986a) reports the frequency of pneumonia to be 14%, this

represents the risk per 100 live born calvings and not an incidence density. A more

78
comparable reporting of monthly incidence densities is reported as approximately 8%

(Waltner-Toews et al, 1986b) The rate of 7.4 reported by Curtis et al. (1988a) seems to

 

represent a six month risk or the rate per 100 half years, Since the denominator reflected
the number of animals at risk during the designated 6 month season.

The effect of having hired personnel (OHIREPOS) caring for the animals had
no significant impact on the occurrence of respiratory disease in calves (Table 5.1) This
is somewhat of a contrast to previous reports; however, these reports were focusing on
calf mortality versus incidence of respiratory disease (Withers, 1952; Oxender et_a_1, 1973;
Hartman eLei, 1974) More recent reports from, prospective studies, have agreed with
this paper and shown no effect of the person caring for calves (Simensen, 1982;
Waltner-Toews gel, 1986c) The effect of this factor in cows was significant (p = .014),
but not in young stock. This factor has not been previously studied in animals older
than calves. ‘

The effect of type of calving facilities (CAVFAC) was important with respect
to disease incidence in calves. This is not surprising, as it has been reported that
cleanliness (Simensen, 1982) and the ability to receive adequate colostrum are important
to calf health. The estimated odds ratio for multi-animal maternity facilities
(MULTMATN) in calves was 10.6 (significant, p < 0.1) This risk enhancing effect of
multi-animal or group calving pens has been observed elsewhere (Ferris and Thomas,
1974; Curtis e_t_al, 1988b) It is interesting that, in the GLM model, having individual
calving stalls only (INDVSTAL) significantly reduced the rate of disease. In the logistic
model, hOwever, the variable INDVSTAL did not have an odds ratio significantly
different that 1.0. The conclusions are the same with both models; that MULTMATN
increase the risk of disease and INDVSTAL does not.

Whether or not MULTMATN produces a risk in adult cows is debatable
(OR=1.7), however the variable CAVFAC (in GLM) did have a significant (p = 0.02)
effect on the annual incidence density of disease in the cows.

The effects of housing are not conclusive for any of the three age groups, although

some trends can be suggested. HUTCHCAF had some tendency to increase disease in

79
calves, and housing of calves with the cows seemed to prevent disease. Housing of
calves in the stanchion with the cows has been reported to decrease mortality (Oxender
et_ai., 1973; Speicher and Hepp, 1973) Loose housing (LOOSE) had some effect at
decreasing disease in cows. The reason is not clear since one might expect freestalls to
be as well ventilated as loose housing.

In youngstock the variable HAYSTOROUT contributed significantly (p= 0.07)
to variation in the incidence density and had an odds ratio of 1.52 with a confidence
interval (50, 4.6) that tended to be greater than 1.0. The hypothesis is that hay which is
stored outside and is uncovered is of less nutrient value than protected hay, thereby
increasing an animals risk for disease and might be more susceptible to molds. This
should be investigated further.

In calves, it is interesting that DISINF tended to be protective for respiratory
disease. It is not clear how occasional disinfection of the maternity area would prevent
the spread of respiratory disease. Most likely, this variable reflects the overall quality
of farm management which might tend to reduce disease. The pernicious effect of
COLSTUBE in calves, "which was shown here, has been reported elsewhere
(Waltner-Toews M, 1986d)

Most of the odds ratios that were estimated had 90% confidence intervals that included
1.0. Some might judge these variables as "insignificant." However, it is possible that with
a larger sample size, these variables would have become "significant." The fact that the
variables were "significant" in the GLM model suggests that the estimated Odds ratios
are valuable but not as precise as could be estimated with more data.

The use of the general linear model, which is simply a linear regression that
automatically creates dummy variables for categorical factors, is justified even though
the dependent variable (ID) was not distributed normally. If distribution of the errors
or residuals is normal, then the model is acceptable (Neter and Wasserman, 1974) The
distribution of residuals was checked for all three final models, with PROC
UNIVARIATE (SAS, 1985), and found not to be deviated from normality (p< 0.02)

The slightly different results obtained between the GLM and the conditional

80
odds ratio can be explained by differences in coding of the dependent variable. In GLM
the dependent variable was continuous and as much information as possible is derived
from any Observation whereas dichotomization (DPOS) of the incidence rates tends to
reduce the amount of information derived from an observation. Also the fact that the
PHGLM used a data set that was assumed to be "matched" for herd-size strata, reduced
the effective sample size and decreased the chances of finding a "significant" result.

The use of conditional estimation accounts for the fact that the small sample
size and large number of variables precludes the use of parametric tests such as the
Chi square. The procedure is an iterative maximum likelihood estimation that assumes
the marginal totals are fixed for each stratum. This is similar to the Mantel-Haenszel
procedure and gives asymptotically similar results. It is generally observed that
unconditional estimates tend to overestimate the Odds ratios for small sample sizes,
compared to conditional (Kleinbaum et_ei., 1982:492-503) Therefore, the odds ratios
reported in this paper may be smaller than those that would result with the use of
unconditional estimationon‘ a larger data set.

The NAHMS data‘gare generally evaluated relative to the quality of the disease
rates and costs that are estimated. If the purpose of the NAHMS is strictly estimation
of the incidence and costs of endemic diseases, (Glosser, 1988) then these data, from the
Michigan project, were relatively useful. However, for purposes of risk factor elucidation
and estimation of the relative effect of various factors, some shortcomings were noted.
A fairly large amount of data were collected on the dependent variable, incidence
density of respiratory disease, but a limited amount of data were available for possible
risk factors, or independent variables. The presence of most risk factors was determined
by the one time management survey. In Michigan, individual cow data were available
and could have been analyzed, but this was not available for calves and youngstock.
Also, in this project, data on the occurrence of disease and animals inventories was
collected monthly, but no monthly data were collected regarding the presence of possible
risk factors. The sample size, of only 48 usable herds, resulted in estimates risk factors

that appeared important, but were not statistically significant.

81

In order for the National Animal Health Monitoring System to provide a valid
database for epidemiologic efforts beyond descriptive statistics (Farrar, 1988) some areas
could be strengthened by: 1) beginning the project with a narrowly defined disease
syndrome to be analyzed, and a clear set of hypotheses to be tested, 2) collecting input
or risk factor data concurrently with output or disease frequency data, 3) providing for
standardization of input, as well as output data, to allow for aggregation of data across
states and data collection rounds, 4) considering individual animal identification where
appropriate, and 5) developing dynamic analytical techniques to evaluate the
implications of the project’s findings in reference to disease control and economics
(Riemann, 1988) All of these activities could still be implemented within the broad

scope of disease frequency and cost estimation.

CHAPTER 6
A Stochastic distributed delay model of disease processes in dynamic populations

ABSTRACT

A simulation model that is applicable to infectious and noninfectious disease is
proposed. The objectives of this paper are to describe a model for simulation of
infectious and noninfectious disease processes in dynamic populations using a distributed
delay (DDEL) approach, and to compare its behavior to a stochastic version of the
Reed-Frost model, for a hypothetical infectious disease. This model represents the main
theoretical subunit of an applied model to be discussed in a subsequent paper.

The distributed delay as an aggregate approximation of the transitions of
individuals through multiple disease states. The average waiting time until disease
occurrence and time to recovery from disease are the delay (DEL) parameters used in
the model. The ability of the distributed delay to simulate the stochastic nature of these
waiting times is investigated, and the epidemic threshold theorem is applied in the
model.

Monte-Carlo simulations of both modeling approaches were run to produce
epidemics of randomly determined sizes. Both models demonstrated the characteristic
bimodal distributions of total number of cases per epidemic, although the shape of the

distributions was slightly different.

INTRODUCTION

Epidemiologic simulation models can _be generally categorized into mass action,
chain binomial, and a general group of models resulting from the systems approach
(Chapter 4) Most applications of simulation modeling of epidemiologic problems have
been to project the course of infectious diseases. This is probably due to the fact that

both the mass action and chain binomial models are based on the premise of

82

83
interactions between infectious and susceptible individuals being the driving force for
dynamic phenomenon. The basic mass action equations for the susceptible, infected,

recovered (SIR) model are shown in equations 61 - 63.

d8
— = -B"S"I (6.1)
dt
(11
— = B'S‘I - 7‘1 (62)
dt
dR
_ = 7‘1 (63)
(it
where:

# susceptible or nonclinical
# infected or clinically ill
# recovered

infectivity parameter

recovery parameter

.21»me

One can see that the incidence rate (dS/dt) is a function of some interaction,

defined by B, between the infected and susceptible individuals. The exact
epidemiological meaning of this B term is not clear (Fine, 1982) It has been called

the ”infectivity", the "transmission coefficient", and the ”transmission rate", and the

"force of infection”. If one assumes completely random and homogeneous mixing

between individuals, this B parameter reflects a characteristic of the disease agent

regarding its ability to spread between individuals, with or without direct contact
(Riley, 9341., 1978) 9

A commonly employed type of chain binomial model, the Reed-Frost model,
is shown in equation 64. The meaning of p, in this equation, represents the
probability of effective contact. The assumption is that contact will always result
in transmission of disease, hence it reflects two separate and unrelated

phenomenon, the mixing characteristics of the population and the transmissibility

84
or infectivity of the organism. The Reed-Frost model also assumes that the
infection duration is relatively short, one time period, and that a single attack of
disease produces lasting immunity (Abbey, 1952)
I(t+1)=S(t)‘[1-(1-P)“"] (6.4)
where: p=probability of effective contact
S=# susceptible or nonclinical

I=# infected or clinically ill

A model applicable to infectious and noninfectious disease is proposed.
The objectives, of this paper, are to use a distributed delay (DDEL) model for
simulation of infectious and noninfectious disease processes in dynamic
populations and to compare the model’s behavior to a stochastic version of the
Reed-Frost model, for a hypothetical infectious disease. This model represents

the main theoretical subunit of an applied model to be discussed in Chapter 7.

MATERIALS AND METHODS
Disease process as a distributed delay

The process of disease occurrence for infectious disease, parasitic disease
(Cohen, 1977), or for cancer, can be viewed as a set of multiple transitions from
one state of development to the next. For example, cancer development, can be
seen in terms of initial onset of disease resulting from some exposure, followed by
progressiOn to clinical manifestations, followed by death or recovery (Morrison,
1979) 7 Infectious disease can be viewed as the movement from the state of
susceptibility, to latency, to incubation, to clinical infection, to recovered, dead, or

immune as shown in Figure 61 (Nokes and Anderson, 1988)

 

 

 

 

 

 

 

 

 

l I I
I
I g .
:3 I | I o I R
=I 1, | 5 , INFECTED [—9
n- O I .- "'
o | a e: I o
0 O I O ' .D
In I a. «s- 3
5 x | a | 3
Lu: l ..I l ._ '
NONCX CLINICAL
Figure 61 Infectious disease application of the proposed distributed delay

model. NONCX = Nonclinical state, CLINICAL = diseased

These transitions can be observed within a population as various rates; for
example, the clinical incidence rate (IR) represents the movement from the
nonclinical state to the clinically affected state, the seroconversion rate represents
movement from the latent to the immune state. The experiences of a single
individual within this population can be represented as a queuing process where
the transition from one state to the next is accomplished at some sort of a "server"
(Ross, 1985) This is analogous to shopping in a supermarket, where an individual
may go to a number of random servers such as the meat service counter, wait to
be served, then move to the produce department, and finally the checkout stand.
The time to exit from the store, or total shopping time, is the sum of the waiting
and service times (random delays) at each server. If one is observing the exit rate
of a large number of people from the shopping center, measurement of the exit
rate represents an observation of the average shopping time for the average
individual, which is the aggregate of a number of separate waiting and service
times that occurred at each server. For an infectious disease, these transitions
might involve the waiting time to exposure, the event of exposure, the time in the
latent state, the incubation period, and finally transition or "exit" to the clinically

infected state (Bartlett, 1953) The transition to clinically infected is termed an exit

86

because it is this transition that is readily observable in a population, ie, the
incidence rate of clinical disease. Commonly, the first set of transitions, before
infection, is not observable and can be viewed as one aggregate state, like the
shopping center.

Since the disease experience in a population can be viewed as a process
of multiple individuals moving from server to server (state to state), a continuous
time model which simulates this process should be beneficial. This model should
adequately reflect the random process of delay at each server, for each individual,
and the experience of movement through multiple servers. The distributed delay
has been shown to be appropriate for representing a variety of aggregate
stochastic processes (Manetsch, 1966) Given the probability density function and
the average waiting time (DEL) for the aggregate process, we can simulate it with
a distributed delay.

The distributed delay used in this simulation model is an Euler numerical
integration (Hamming, 1962) of the k“I order differential equation shown in
equation 65. The Quick Basic (Microsoft, 1988) subroutine for simulating this
equation with time varying delay and proportional losses is shown in Appendix
C. This model is useful for representing a wide variety of processes such as the
maturation process (Plant and Wilson, 1986), diffusion of ideas (Manetsch, and
Park, 1977), many entomology simulation models (Kitching, 1983), and transitions
between different disease states. Many different delays can be linked together as

long as there is information to parameterize them, ie, to set the delay and the k.

d"(t) dk-1y(t)
ak——+ak-1———+---+a,y(t)=x(t) (65)
dtk dt"-1
x(t) = the input at time t
y(t) = the output at time t
k = the order of the defining differential equation
ak = the k specific parameter defining the response of y(t) to x(t)

The model proposed in this paper, consists of 2 distributed delays in series,

(Figure 6.2) The first distributed delay, NONCX (nonclinical), represents

87
individuals in a population susceptible to clinical disease. The second distributed
delay, CLINICAL, represents individuals diagnosed, by clinical signs, to have the
disease. The rate Of movement between the two populations is measured by the
incidence rate (IR) After a certain amount of time in CLINICAL, individuals
are removed from this state. At this time they may be immune, dead or susceptible
again. These suseptibles could cycle back into the first distributed delay and
become repeat cases or go to other states. This option was not implemented in
this chapter in order to provide a comparison to the Reed-Frost SIR (Suspectable,

Infected, Recovered) model (Ackerman, et al, 1984)

 

 

 

 

 

 

 

 

 

CLINICAL a
”000/10/60/ INCIDENCE fi) Clinical/y ‘
Individual: RATE Affected
Individuals
NONCX CLINICAL
DUEL DDEL

Figure 6.2 Schematic diagram of proposed distributed delay model for
infectious and noninfectious diseases. NONCX = nonclincal

.The average time individuals spend in CLINICAL is the average duration
of disease (IDUR) which represents the delay (DEL) for that distributed delay.
The average time in NONCX is the delay (DEL) for that state. Calculation of this
DEL, for an infectious disease will be discussed.

The use of the distributed delay for the CLINICAL state has been
proposed by others (Hethcote, e_Lel, 1981; Hethcote and Tudor, 1980), however its

88

application to the susceptible or nonclinical disease state (NONCX) has not been
attempted. This application has the advantage of being useful for modelling
infectious as well as noninfectious diseases in populations. This works even if the
rate of transitions between various states, within N ONCX, is not observable. The
stochastic processes of multiple individuals moving through multiple states, or
arriving at multiple servers can be realistically approximated by a distributed
delay.
Esiiipatiop of ihe output gistribuiiep

The magnitude of k determines the distribution of the output. If, for
example a group of individuals were simultaneously added to a distributed delay,
the deterministic output for different values of k, but the same average delay
(DEL) is shown in Figure 63 (Manetsch and Park, 1972) Figure 6.3 shows the
family of Erlang distributions which can be represented by a distributed delay.
Determination of the best value of k to use for a particular application can be a
difficult issue, unless one can make observations on a number of individuals
simultaneously entering NONCX, all of whom are known to be susceptible and in
the same stage of disease development. The shape of the output for a constant

DEL will indicate the best k to use.

89

 

 

 

it?)
I‘\ k'25
/ \
I \
I \
I \
I \
I \
I \
I, \
\k.l // I \\\\
‘ x I I k=6 \
, C V a
, ‘- L _ I / ~ ‘\ \
/ \- - — _\~:~
I / I ‘ \ - a. ‘—
1" / v’ ’4 l/ j l l ~-§=--—‘7’
617']
Figure 6.3 Family of Erlang distributions for waiting times to exit, which can

be represented with a distributed delay. E[T] = average waiting time
to exit. (Manetsch, 1966)

For a hypothetical population of known healthy people, Rothman (1986) has
shown that the time between deaths is exponentially distributed with mean 1/IR
(IR = incidence rate) This is equivalent to a k=1 distributed delay, with unit input.
This would be analogous to a single stage server where each person was assured
the event, death, and the only thing that was random is the waiting time to exit.
These waiting times, are generally assumed to be an exponentially distributed
random variables (Ross, 1985) Most diseases usually involve multiple transitions,
or visits to exponential servers, so that k=1 is not universally appropriate. The
sum of multiple exponential distributions is an Erlang distribution, if all waiting
times are equal (Law and Kelton, 1982), or gamma if the waiting times are
different.

It should be noted that the distribution being approximated is not the epidemic

curve, but the distribution of waiting times until exit from the NONCX state if

90
a number of individuals enter simultaneously.

For the second delay, CLINICAL, the distribution can be defined by
estimating the shortest and the longest time that an individual might stay in this
state given assumptions of the average infection duration. Three combinations of
k=1, k=6, k=20 were evaluated, in the model, for each state CLINICAL and
NONCX.

sti 'O o

The Incidence rate (IR) or density (ID) represents the average waiting time
until disease occurrence, for a steady state dynamic population, or a fixed size
population with complete follow-up (Morrison, 1979; Rothman, 1986) The ID is
calculated as (sum of cases/ sum of observation time periods for all individuals)
Therefore, the inverse of the IR, theoretically, will provide the needed DEL for
the NONCX distributed delay. Since the units of the ID are the reciprocal of
time, the delay is expressed in those time units. For example, if an IR is reported
as cases per animal years, the DEL is expressed in average number of years an
animal is expected to spend in the NONCX state. It is important that the method
used to calculate the IR’S are appropriate to the time frame of the model (Hurd
and Kaneene, 1989a)

The mathematical relationship, between DEL for NONCX and the IR can
be used to derive an equation to generate a time varying DEL for infectious
disease models. In this case, the incidence rate, or number Of new cases per time

unit is defined by the relationship between the number of infectious individuals,
and the infectivity (B) as in the mass action and chain-binomial models. For the
distributed delay model proposed in this paper it is necessary to derive an equation
for computing a DEL in the same manner. It is stated that for the mass action
model IR = B "‘ S(t) * I(t), and for the Reed-Frost or binomial models IR =
C,+1/S(t) = 1-(1-p)I(‘). For small values of p and/or large populations, the Reed-

Frost and mass action models are essentially equivalent (Fine, 1982) but the Reed-

Frost performs better for small populations (11 < 40) (Bailey, 1955) Therefore we

91
can derive a method for computing the delay at time = t, DEL(t), as a function of
the number of infectives at time=t, I(t), by using the Reed-Frost model. As shown
in equation 66, the waiting time (DEL) will decrease as the number of infecteds
increase, hence more individuals will get sick faster, producing the classic epidemic
curve. The probability of effective contact (p), from the Reed-Frost model is not
used in equation 6.6, as it is not clear that B has the same properties as p.

1
DEL(t) = (6.6)

1-(1-B)“"

 

' mic h es 0] the ied
An important phenomenon of infectious disease process is the epidemic
threshold theorem (McKendrick, 1926; Becker, 1979, Fine, 1982) This theorem states
that for an epidemic to progress, the probability of infection must be greater than
the probability of recovery, ie. the odds of a new case should be greater than 1.

A certain number of suseptibles is required to meet this condition, this number,

or threshold, is determined by the ratio of the recovery rate (7) to the transmission
factor (B) such that S(t) < ‘y/B, where the recovery rate (7) is the inverse of the

infection duration (IDUR) If 'y and B are constant characteristics of the disease,

the demise of an epidemic is the result of a decrease in the number of suseptibles,
not in a decrease in number of infectives. This relates to the concept of herd

immunity that suggests adequate vaccination should proceed to the point where

the number of suseptibles is less than 1/B (Fox, ei e1, 1979) This threshold

theorem has been shown to be applicable to continuous or discrete time mass
action models (McKendrick, 1926; Fine, 1982) as well as non-Markovian and
Markovian continuous time models (Becker, 1979)

Simulation of this phenomenon is straightforward with the Reed-Frost
model. The computer program is equipped with a stopping rule that causes the

process to stop if there are no new cases produced at time t+1, C,+l = 0. For

92

continuous time mass action models the conditions for epidemic shut off have
been mathematically established, but an equivalent expression is needed for the

distributed delay model. Mathematically the continuous mass action model
predicts an increase in the incidence as long as the S(t) > ‘y/B (Fine, 1982) The

determination of an equivalent expression, for this threshold, that is pertinent to

the distributed delay model of disease is shown in equation 67.

(II
—— = 0 , when B‘S‘I = 7’1 (67)
(It

ti to ast'cit

Stochastic versions of both the mass action and chain binomial models
have been studied (Bailey, 1975; Ackerman, MI. 1984) Most of the mass action
stochastic models have studied the number infected or susceptible individual as the
random variable and sought analytical solutions to the equations. The Reed-Frost
simulation model used in this paper generates a uniformly distributed random
number for each susceptible, at each iteration. This random number (RND) is
then compared to the current probability of escape q(t) = (1-p)'(‘). If RND is
greater than q(t) then a new case is added.

In the proposed distributed delay model, stochasticity is implemented by

allowing the beta (B) to vary randomly. This represents the uncertainty in the
value of B as well as the random error for any individual in a population. The

model ,was run with a triangular distribution as shown in Figure 64 or an

exponential distribution assigned to the B. The effects of different distributions

on the number of infective contacts along with more rigorous mathematical theory

are discussed elsewhere (Dietz and Schenzle, 1985)

93

fl?)

2
max-min

 

_-—-------

 

 

 

. 7-
0 MIN MODE mm

Figure 6.4 Triangular distribution assigned to B. The minimum (MIN),
maximum (MAX), and MODE must be defined.

d 0 'so
The Reed-Frost computer model outlined in Ackerman, et el. (1984), page
34 was compared to the proposed distributed delay model. Monte-Carlo runs of

the models were implemented for 100 epidemics. Different values for p, in the
Reed-Frost, and distributions of B, for the distributed delay model were compared.

The goal was to reproduce the characteristic frequency distributions of total
number of cases per epidemic observed with the Reed-Frost model. Also the
average attack rate for 100 runs was compared between models, where the per
epidemic attack rate = sum cases/total population size.

Different settings for the k in NONCX and CLINICAL were evaluated
and distributions compared to the Reed-Frost. All combinations of values of k=1,
k=6, and k=20 were evaluated. Model runs were carried out on a microcomputer

with Quick Basic (Microsoft, 1988) as the programming language for the distributed

9.4
delay and Pascal for the stochastic Reed-Frost model (Foster, 1984) All

populations started with 1000 susceptible individuals and 2 infectives.

RESULTS
A comparison of average attack rates and number of epidemics with total
cases less than fifty, for different parameter settings is shown in Table 61. Results

of the average attack rates for the Reed-Frost are similar to those of the
triangularly distributed B, for the same value of p or B. However, average attack
rates from the exponentially distributed B were much higher, and the number of
epidemics with less than 50 cases was lower than for comparable values of p or

triangular B.

Table 61 Comparison of Reed-Frost and distributed delay stochastic models.

 

 

 

Reed-Fm Distributed delay
Average No. epidemics”
Average. No. epidemics attack with <50
attack with <50 rate cases
p rate cases B Expo Tri Expo Tri
.0016 .58 10 .0016 .76 .57 8 I9
.0012 .15 50 .0012 .60 .18 21 52
.001 .03 78 .001 .49 .03 33 86
.(XJO8 , .013 95 .0008 .39 .015 99 99
.0004 .005 100 .0006 .22 63 0

 

‘Aversgeanackrate -NRUN mmof
E cases/populationsize ,NRUN-lofsinmlationmns
1
p - pmbabilityofeffecitvecomactforReed-Frost 8(0) - 1000,1(0) - 2
B I: infectivityparameterfordinributeddelay

“NunterofepidemicswithlessthsnSOcases

Histograms comparing the frequency distributions for the Reed-Frost,

DDEL with a triangularly distributed B and an exponentially distributed B are

95
shown in Figures 65 - 6.8 The values of k =6 were used in the distributed delay
simulations. Values of k = 1 did not display as pronounced of a bimodal
distribution, and values of k=20 produced computational problems due to the lack
of conservation of flow as a result of the random changes in the delay.

The histograms from the distributed delay model (exponential and
triangular) Show the desired bimodal distributions. The details of the DDEL plots
do differ somewhat from the Reed-Frost model. For example, the triangular B
= .0016, (Figure 65) the separation between the two peaks is not a great as the
Reed—Frost. This not surprising since the distributed delay is continuous entity

model, ie. it uses real numbers instead of integers, resulting in a smoother curve.
For B = .0012, triangularly distributed (Figure 66) the tail is slightly more extended
and there are more epidemics in the 50100 case range, but the bimodal distribution
is still evident. The exponentially distributed B also demonstrated the bimodal
distribution (Figures 67-68, top graph) The spread between the two peaks is more
pronounced than the triangularly distributed B and than the Reed-Frost. Figures

67 and 68 compare distributions between the two models that produced similar

average attack rates (see also Table 61)

Figure 65

DDE L
A = .0016

 

”firm I 11 WW I

no. or l9 s l
EPIDEMICS 4 3 l I 2 3377613'5
Reed-Frost
fl=.00l6 I

 

 

 

 

 

 

II” H
aaasrzsszsssasassm
EPIDEM 556??“ -nI’I’n"’°°'f

IC ”0° OOSOOIII 1°
unn'Qggogh

N0.0F D l 35 5
EPIDENICS 9 42

Frequency distributions (100 epidemics) of distributed delay (DDEL)
(a) and Reed-Frost (b) stochastic disease models for p = .0016 and
B=.0016, TRIANGULAR distribution

DDEL
fl =.0012

 

 

 

 

 

 

 

 

N0.0F sz 3
EPIDEMIcs a
Reed-Frost
F=.OOI2
HIHHHHHHI
TWALm.°F08GOQOOQQOGOGOOgO
mssseeanSQSSI'I'Igzgi'ISBSIAS
trim-c osg'gaaaasaasaaaa'g
__ O
83n3398388228
N0.0F so I 4 la 4
EPIoemcs 3 3 ll 10 I

Figure 6.6 Frequency distributions (100 epidemics) of distributed delay (DDEL)
(a) and Reed-Frost (b) stochastic disease models for p = .0012 and B
= .0012, TRIANGULAR distribution.

\V—
\

DDEL
I = .0006

 

 

 

 

542 Illll I

 

 

 

 

 

 

Numberot 63 2 7 ll
Epidemics
...,
Reed-Frost
p=.OOl2
1
. nfinflH flfln
Total Number of o o o o o o o o o
CaseeperEpIdemlc93253§§33§3§33 gag
OLE'LIL'LLL' '0'
In .. - - - - _
288338988 838
Numberot
Epidemics 50 3 l 3 4 II i6 IO 4 I

Figure 6.7 Frequency distributions (100 epidemics) of distributed delay (DDEL)
with EXPONENTIAL distribution (a) and Reed-Frost (b) stochastic

disease models for p = .0012 , B = .0006

DDEL
fl =.OOI

 

Number of 33 2
Epidemics

Reed- Frost —
p= .0016

 

 

 

 

H .HH [1
TotslNumberoi °8 °S°°°°8° cocoooo
Cases per Epidemic '0 _ O o In 0 n n n O on o o
6;, ttrrrfi’i’éft'zrrf‘g
not-36363656100383
- or
Numberot NMnflV'flfi‘choo
Epidemics I0 I9 35 425

Figure 68 Frequency distributions (100 epidemics) of distributed delay (DDEL)
with EXPONENTIAL distribution (a) and Reed-Frost (b) stochastic
disease models for p = .0016 , B = .001

100

DISCUSSION

It is not necessary that matching B and p should values should produce the

same distribution, or same average attack rate, as the meaning of the two values

is different. It might be expected that a value for B lower than p would be

required to produce the same average attack rate since the distributed delay model
tends to retain individuals in the infected state longer than the Reed-Frost model
which assumes infectivity lasts one discrete time period. This was noted in the
exponentially distributed delay. The triangular distribution was set with upper
limits much lower than those permitted with the exponential distribution which
theoretically has no upper limit. This explains the higher attack rates and wider

spread to the bimodal frequency distribution observed with the exponential.

The best distribution to use for B should be determined by its distribution

in the system which is being modelled, not by comparing it to another theoretical
distribution. A definition and estimation of B and its distribution will be discussed

in Chapter 7.
An advantage of a distributed delay model is shown in that, depending on

the k, the infection duration (IDUR) can actually be randomly represented. For

example, if the mean IDUR is 7 days ( E[T]=7) and k=6, some individuals will

start to leave the state in only 2 days and others will stay much longer (Figure
6.3) It is thought that these distributions allow for more realistic models than
most mass actions models which assume an exponential distribution of IDUR, ie.
k=1 (Bailey, 1975)

A disadvantage of the distributed delay may be that it is more
computationally complex and stability criterion must be carefully monitored. As
a continuous entity model there is some aggregation error, especially for small
populations. That the output of the distributed delay are represented by the

family of Erlang distributions assumes that the waiting times at all "servers" within

101
the state are equal. A gamma distribution might be more realistic, if the waiting
times at each "server" were known to be different.

Other advantages are that it is useful for infectious or noninfectious
diseases. It represents the stochastic nature of waiting times until disease
occurrence and exit from the nonclinical state, and allows flexibility in defining
the distribution of the outputs by altering the k value. It can realistically
accommodate other vital dynamics, such as birth or migrations into the
populations. The computational speed of the model is not affected by the number
of individuals in the population as are other discrete entity models (Chapter 4)

That both models demonstrate the threshold phenomenon has ramifications
for all epidemiologic studies of infectious disease. For example, statistical analysis
of the effects of various factors on the incidence of disease between two
populations could be biased by this threshold phenomenon, since the errors will
not be distributed normally. For example, two populations with the same set of
risk factors might have very different rates due just to chance, as each epidemic
falls in a different peak of the bimodal distribution. The effects of this
phenomenon on infectious disease analysis need further investigation.

It is hoped that this distributed delay model of disease processes will
provide a generic model for simulation of disease processes in dynamic
populations of a various types. The applicability of this model will be investigated

in the next chapter.

CHAPTER 7

Application of a stochastic distributed delay simulation model to the epidemiology of

clinical respiratory disease in a dairy cattle population.

INTRODUCTION

The various type of epidemiological simulation models have been described in
Chapter 4. The data collection process, descriptive epidemiologic and economic statistics,
along with a critique of data quality have been discussed in Chapters 1 and 3. A generic
model for disease processes in dynamic populations has been described and tested in
Chapter 6 The objectives of this chapter are to describe the application of the model
in Chapter 6 to clinical respiratory disease in a typical Michigan dairy cattle herd. The
predictive ability of the model will be tested against the database described in Chapter
1 and 3.

MATERIALS AND METHODS
Mode] descsipiion

According to the proposed epidemiologic model classification scheme in Chapter
4, this model can be classified as a stochastic structural process model with continuous
time and entity computation by simulation.

The distributed delay model, proposed in Chapter 6, is applied in this model to
represent the 3 age groups of cattle defined in the NAHMS database. Additional states
of disease, such as IMMUNE and RECOVERED are defined along with the CLINICAL
and NON-CLINICAL states. Most of the disease states are implemented with the time
varying distributed delay of Chapter 6, however, the additional feature of proportional
losses from the delay are included to allow for aging and losses from the populations
(Manetsch, 1976) A detailed block diagram of the dairy herd, is shown in Figures 7.1 a-

c. Each figure represents one age group, but the groups are interconnected so that

102

103

animals can grow into the next age group. The assumptions and definitions for each age
group will be discussed below.

Calves are defined as animals from birth until weaning. Calves can fall into 4
disease states, CLINICAL and NON-CLINICAL, IMMUNE due to infection, and
COLOSTRUM-IMMUNE due to intake of colostral antibodies. NON-CLINICAL
Calves are assumed to be susceptible to disease (S), and are noninfectious. CLINICAL
Calves are presenting overt signs of respiratory disease, such as coughing, runny noses,
respiratory distress, or any other signs consistent with a diagnosis of upper or lower
tract respiratory disease. CLINICAL Calves are spreading the disease to other animals
in the herd, therefore are considered infective (I) IMMUNE Calves are those that have
passed through the CLINICAL state and are resistant to reinfection. Some of these
animals may have a decrease growth rate and will be weaned at a later age, these are
classified as "poor doers". Since it is assumed that the duration of immunity (270 days)
is longer than the time to weaning (90140 days) these Calves will be weaned into the
IMMUNE Young Stock state and do not have a chance to return to the susceptible
state. The impartation of natural immunity from antibodies in colostrum is considered
to play an important role in the epidemiology of respiratory disease ( Miller, ell, 1980)
For this reason, the state of COLOSTRUM-IMMUN E was included to represent those
animals born of IMMUNE or VACCINATED cows. The duration of this natural
immunity is estimated from the literature to be 60 days (Radostitis and Blood, 1985)
COLOSTRUM-IMMUNE Calves are moved into the NON-CLINICAL state after an
average 60 days, and become susceptible to infection.

Calves are born into the NON-CLINICAL or COLOSTRUM-IMMUNE states
at a daily rate determined by the number of cows present in the herd. Calves born of
cows in the IMMUNE state go into the COLOSTRUM-IMMUNE state for Calves, and
Calves born from CLINICAL and NON-CLINICAL cows go into the NON-CLINICAL

state.

104

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Epidemiologic simulation model of the Animal Population and Production

System (APPS) for CALVES.

Figure 7.1a

105

By application of the proportional loss feature of the distributed delay, animals
are removed from each of the above states. Some of the Calves are weaned into the
various Young Stock states, others die, poor doers are culled, and Calves are sold at the
observed sell rate, which includes bull Calves sold Calves in the CLINICAL state die
according to the case fatality rate observed in the NAHMS data. The case fatality rate
for all age groups can be altered for economic analysis of the effects of veterinary
intervention (Chapter 8). Default values used for parameters in the model and their
source are shown in Table 7.1. Some of these parameters were reset when herd specific
simulations were run.

For Young Stock, animals from weaning to first calving, the 3 states, NON-
CLINICAL, CLINICAL, and IMMUNE are defined the same as for Calves. Young
Stock can also be vaccinated at any user defined age level, at which time they will move
into the VACCINATED state. Since animals can be Young Stock for 19-25 months, it
is possible that immunity from infection, or vaccination, may decrease to the point that
they may be again susceptible to disease and return to the NON-CLINICAL state.
RECOVERED Young Stock are those that have had clinical disease, developed, and lost
their immunity. A certain proportion of the IMMUNE and RECOVERED ("poor
doers") will have a reduced growth rate and later freshening age than the NON-
CLINICAL and CLINICAL. This proportion is reflected by increasing the freshening
age for those 2 states according to the poor doer rate and the percentage decrease in
growth (Table 7.1).

Young Stock states receive newly weaned Calves from the same respective
disease states from which the Calves were located at weaning. Young Stock that freshen
go into the same respective state for Cows, except for RECOVERED Young Stock
which freshen into N ON-CLINICAL cows. Losses due to non respiratory culling, and
non-respiratory mortality occur from all states. Respiratory mortality (case fatality)
occurs in the CLINICAL state only, and respiratory related culling relates to poor doers

in the RECOVERED and IMMUNE states (Table 7.1)

106
legend

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Epidemiologic simulation model of the Animal Population and Production
System (APPS) for YOUNG STOCK.

107

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

    
    

 

 

 

 

 

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Epidemiologic simulation model of the Animal Population and Production

System (APPS) for COWS

Figure 7.1c

108

In Cows, animals after first calving, the disease states are the same as in Young
Stock with the exclusion of the RECOVERED state. It is assumed, based on the
authors clinical experience, that most respiratory disease in adult dairy cattle does not
impair long term performance, so the RECOVERED state was not needed. Animals
in the NON-CLINICAL and IMMUNE states will produce milk at a user defined daily
rate, and those in the CLINICAL state will produce milk at a decreased rate (Chapter
8)

For all 3 age groups the length of the delay in NON-CLINICAL is set at some
starting level. This initial value can be set as a function of the observed annual
incidence density or a prediction from the linear regression equation of Chapter 5. This
delay is then altered as a function of the number of individuals in the CLINICAL state
as described in Chapter 6 and equation 7.1. This in effect represents a feedback loop as
shown in Figures 7.1a-c.

1
DEL(t) = (7.1)

1-(1-B)“"

 

Computational methods

The early versions of the model were designed and tested on the Apple
Macintosh SE with a graphic simulation software program (STELLA, 1987) Due to
computational limitations of STELLA, the full model was implemented with Quick
Basic (Microsoft, 1988) A 365 day run on a Compaq 386, 25 megahertz clock speed with
a math coprocessor, took about 8 minutes. The delta time (dt), for numerical integration,
was set at 0.1, so each day of simulation required 10 loops through the model.

The mathematics and behavior of the distributed delay is described in Chapter
6. However, for Young Stock, a unique modification was made to the distributed delay
routine. This modification is called the double delay and its subroutine is shown in
Appendix D. The double delay manipulates an array of animals each cell of the array

designates a different KI stage of disease progression (Chapter 6) and KA level of

109
maturation. The number of animals in any cell is computed with Euler integration
similar to the distributed delay. The subroutine allows for bilateral movement for
animals, along the disease progression and maturation processes. It also allows for
selective age level vaccination. The user can choose the age range at which Young
Stock should be vaccinated and only those animals stored in the appropriate KA stage
of the delay will be removed to the VACCINATED state. Since the transit time for an
animal from a newly weaned calf to freshening heifer is fairly long (19-24 months) and
variable, it seemed reasonable to allow this process to have the same distributed features
as described for disease processes in Chapter 6. The maturation process is the most
common application of the distributed delay (Plant and Wilson 1986)
r et stimat'o

A majority of the important model parameters were estimated from the NAHMS
data, using average values from all 48 herds with useable data. Those that were not
available were derived from the literature (Table 7.1). For those parameters, such as
infection and immunity duration, which were estimated from the literature, averages
were taken from various authors who were describing separate specific etiologies. For
example, the infection duration for Parainfluenza 3 infection is reported to be 7-8 days
(Gillespe and Timoney, 1981), and 3-5 days for Bovine Respiratory Syncytial Virus
(Mathes and Axthelm, 1985). Duration of immunity was more variable it was reported
as being short for BRSV (Gillespe and Timoney, 1981), and solid but indefinite for
Bovine Virus Diarrhea (Blood, ELEL 1985)

110

Table 7.1 Epidemiologic model parameters.
NAHMS Round I and literature.

Average daily rates from Michigan

 

 

 

 

 

Variable Default Units Comment Source

CALVES

Non-resp mortality .001 hdlday 3 per 100 calf months Data

Non-resp cull rate Q0 hdlday assume not sold for dairy Data

Resp cull rate 6E"6 hdlday .02 per 100 calf months Data

Case fatality rate .02 hdlday 15% over 7-day infection Data

Weaning age 120 days

Late weaning age 140 day Due to a 2-7% decrease Thomas, 1973
in daily gain Miller, 1980

CLOSDUR 60 day Duration of natural Radostits, 1985
immunity from colostrum

Mean SAR .106 Secondary attack rate Data

Prob New .15 % Probability of new infective Data

W

Non-resp mortality 2.4E'5 hdlday 7 per 10,000 animal months Data

Non-reap cull rate 0.0 5 hdlday 6 per 10,000 animal months Data

Resp cull rate 83E'5 hdlday From immune and recovered Data

Case fatality rate .013 hdlday 9% over 7-day infection Data

Freshening age 27 months Assume delay not due to DHIA
respiratory disease

Late freshening age 29 months Based on a 5% decrease in Miller, 1980
weight gain

Mean SAR .019 Secondary attack rate Data

Prob New .07 Probability of new infective Data

gems

Purchase rate variable hdlday Function of number in
animal inventory

Non-resp mortality LOGE" hdlday Data

Non-resp cull rate .0008 hdlday Increase if number in animal

' inventory above starting level

Resp cull rate 0 hdlday

Case fatality rate 2.8E'3 hdlday 2% over 7-day infection duration Data

Mean SAR .005 Secondary attack rate Data

Prob New .06 % Probability of new infective Data

W '

Infection duration 7 days Average time in CLINICAL Literature

Immunity duration 360 days After natural infection

Vaccination duration 270 days

111
Wars

In other mass action models it is stated that the meaning of the B term, or

infectivity parameter is not clear (Fine, 1982) For this model it will be defined as the
classic Secondary Attack Rate (SAR) (Kemper, 1980) which is defined as the propensity
of disease to spread within a population after the introduction of a single infective
individual. This parameter can be estimated from any herd within the NAHMS
database, for any month, as shown in equation 7.2. If one case of disease occurred
within a month the SAR = 0 since this original case generated no new cases. If no cases
of disease occurred the SAR was not estimable, as the lack of an initial case made it
impossible to determine the propensity for disease to spread.

SAR = I - 1/ S-1 (72)

I = the number of new cases durin the month
S = the number of animals at risk Chapter 2)

The frequency distribution of the SAR’s was simulated with exponential

distribution so values for B were randomly generated from a subroutine (EXPON,

Appendix D) with the mean SAR set at the beginning of the run. A new value for B

was generated every 30 days from the exponential distribution. Since the SAR assumes
that one infective is present in every population experiencing disease the model was
altered from Chapter 6 to allow alteration of the delay, by feedback, only if the number
in the CLINICAL state was greater than or equal to 1.0.

The model was usually initialize with one or two animals in the CLINICAL
state, however once this infective recovered it was necessary to allow the introduction
of new infective into the herd. This was accomplished, for each age group, by
calculating the proportion of herd months that had at least one infection in the herd,
and comparing that to a uniform random distribution generated every 30 simulation
days. If the uniform random number was greater than the probability of infection,
one individual was added to the CLINICAL state. In Calves, Young Stock, and cows

the observed probabilities of a new infection were, .15, .07, and .06, respectively.

112
jljesting of the model

In order to test the ability of the model to predict annual incidence densities
(aID) of clinical respiratory disease, data from one herd in each herd-size stratum
(Chapter 1) was compared to 365 day runs of the model. The number of animals in
each age group was set to the average number observed in the herd. Random variation
occurred in the SAR, and addition of new infective. It was necessary to use specific
parameters of cull, mortality, and sell rates for each herd simulated (Table 7.2) This was
done in order to model the population sizes observed in the data.

It is clear from Chapter 6 that the proportion of individuals in the susceptible
and immune states of disease plays a very important role in determining the observed
or simulated frequencies of disease. Unfortunately it was not possible to estimate this
proportion in the herds observed in this project. Therefore when testing the model was
was necessary to evaluate different starting ratios of susceptibles (NON-CLINICAL) and
IMMUNE. A 1:3, and 1:1, ratio was evaluated for each herd. Unlike the model of
Chapter 6, no initial infective was added to the herd as the beginning of the run.

The model was run Monte Carlo for 50 runs of 365 day, for each of the two
starting ratios. A 95% confidence interval was estimated on the aID’s predicted from
the model and this was compared to the observed annual incidence density (aIDobs)

with the confidence interval test (Law and Kelton, 1982).

113

Table 7.2 Observed and simulated annual incidence densities (aID) for NAHMS herds.
Herd specific sizes and loss rate used for each model run.

 

 

12%; Daily Loss rates Susceptible/Immune
er
Age Size NRCull RCull NR Mort a Mort Sell aIDobs n3 1-1
11:02
1 33 o o 835‘5 8315'5 .0043 0044 00891.04? 0231.076'
2 164 335‘5 0 0 o 6.715‘la 0010 00351019 01210?
3 143 o o 1515" o f .0011 0023:.002' 003610020
1501
1 4 o o 0043 .0008 008 02 034303? 0541032
2 l8 0 0 141-3" 0 .00076 00 01591009 021111016
3 26 o o 0022 o f 00 004310013 0048:002
1502
1 a0 0 0 43a“ 0 o .044 0211016 0561.04'
2 73 371-:‘5 o o 0 6.3“ .0057 0223.018‘ 05:01?
3 49 455" 0 115" 0 f 00 00063002? 0019100?
RESULTS ' - observed annual incidence density fell within 95% confidence interval of simulated alD

The mean observed SAR for Calves, Young Stock and cows was 0.106, 0.019, and 0.005.
Most herds had an SAR = 0 with a maximum in Calves = 2.0, Young Stock = .64, and
cows = .43. These maxima were much higher than most of the other observations in
the age group, and were considered outliers and deleted to compute the above means.
The distributions of the observed SARs, minus the outliers, are shown in Figure 7.2.
This was the reason for using the exponential distribution for the secondary attack rates.
Predicted versue eimulated dieeese frequegcies

The observed annual incidence density (aIDobs) for the 3 herds tested fell within
the 95% confidence interval 6 of 9 times, for both ratios, which was not significantly (p
< .01) different from expected of 9 of 9 times, with the Chi Square goodness of fit test.
Producer 15.01 had the fewest number of accurate predictions. The 1:1 Susceptible to

Immune ratio had generally higher predicted aID’s, with wider confidence intervals.

114
rv t' v'

If the mean SAR for the random exponential distribution was set higher than
the observed mean, then a herd might experience high rates of disease in one run of
the model and low to zero rates in the next run. Thus the characteristic bimodal
distribution was observed. The initial incidence density determined the endemic level
of disease in a herd, for settings of the SAR at or below the mean. The SAR’s
modulated the epidemic potential, and the probability of a new infective reflected the

effects of introduction of new infection from outside of the herd.

r.

U data (woe)

N
O
1

OBSERVATIONS

 

 

 

 

 

 

 

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O O’l LI‘Z 2.l’3 31" 4.!‘5 5.!‘6 6.!‘7 71'. 0.1"

SAR Io'I
Figure 7.2 Observed distribution of Secondary Attack Rate in CALVES.

 

DISCUSSION

Herd 15:01 was the smallest herd and had the lowest success rate. This could be
due to aggregation error or failure to include a particular specific herd phenomenon
such as contact between age groups. The use of herd specific cull, mortality, and sell
rates added as much specificity as the data would allow. More data were needed on the

actual ratios of Susceptible to Immunes in a given herd.

115

It seems reasonable to expect that this model could accurately predict the rates
of disease in a given herd, on a monthly basis, provided the appropriate herd specific
data were available. Further statistical analysis that determined the effect of changes
in monthly risk factors and seasonality on herd specific Secondary Attack Rates (SAR)
would allow evaluation of the economic and epidemiologic effect of interventions to
change the levels of risk factors. Analytical techniques that use a process model such
as this one to isolate and estimate dynamic parameters such as the SAR, would be
increase the utility of this model for purposes of risk factor analysis. The integration
of stochastic SAR’s, randomly generated new infective, and a baseline incidence density,
allowed for modelling of the endemic characteristics of this disease while including the
potential of epidemic occurrence.

Many of the parameters used in this model were derived from the original
database to which the model applied. This has the advantage of giving a more accurate
representation of the system in question. Since averages were used from all herds in the
sample, and since the sample was randomly selected to represent the Michigan dairy
population conclusions from the modelling exercise should apply to the "average"
Michigan dairy herd. It was not the intent of this chapter to make conclusions about
the epidemiology and control of respiratory disease in Michigan dairy herds. However,
the following chapter will attempt to make some estimations of the economics of
respiratory disease in Michigan.

For parameters not derived from the data, such as the average infection duration
or duration of immunity, the literature was used to give estimates for what may be
termed ”generic" respiratory disease. The specifics of particular etiologic agents was
overlooked since this accuracy of diagnosis was not available in the data. The
implications of the accuracy of diagnosis for the decision maker are discussed in
Chapter 1. The advantage of this model is that the epidemiology of specific agents can
be addressed with the input of pertinent parameters, and little or no restructuring of the

model.

116

The use of a continuous entity model may have some disadvantages in terms of
aggregation error and lack of the ability to identify individual animal characteristics
(Elveback et_a_l., 1984). However, this type of model is frequently employed in
epidemiology (Chapter 4). It has the advantage of not being computationally slowed or
complicated by the size of the population being modelled. It can readily accommodate
the use of rates and proportions to describe the characteristics of movement, for
example the SAR, culling and mortality rates, estimated from the NAHMS database.
The use of a continuous entity model allows the employ of the distributed delay routine,
which is an important feature in adding realism to the model. For example, the
distributed delay applied to the CLINICAL state, removes a common assumption of
other epidemiologic model, that of an exponential distribution for infection duration in
the mass action model (Fine,1982) or the short and constant infection duration of the
Reed-Frost model (Abbey, 1952, Chapter 4 )

The use of the distributed delay for the NON-CLINICAL state has the advantage
of being useful for modelling non-infectious disease. Since the delay time, or waiting
time in NON-CLINICAL can be described to be a function of other factors within the
herd, such as environment or management, it need not be driven by the number of

individuals in the infected state as do the mass action and Reed-Frost type of models.

SUMMARY

Compared to other epidemiologic models (Chapter 4), this model contains the
realistic representations of the dynamics of disease in a dairy herd. Few models found
include more than one age group of animals, in combination with immigration and
emigration and multiple states of disease susceptibility. The model’s ability to
approximate the endemic and epidemic potential of disease should make it useful for

purposes of economic analysis of disease.

CHAPTER 8

Application of a stochastic distributed delay simulation model to economic analysis of

Clinical Respiratory Disease in Michigan dairy cattle

INTRODUCTION

In Chapter 3 estimations of the "costs" of common dairy diseases were described.
The methods used to define and calculate these costs were designed to meet the needs
of all states participating in the National Animal Health Monitoring System. Certain
shortcomings in the methods used in Chapter 3 were discussed. These include: 1) no
estimation of the long term effects of disease due to lost animal potential, 2) no
measurement of subclinical effects of decreased growth, 3) dependency on producer
estimates of animal value, 4) lack of adjustment for revenue increasing effects of disease,
and 5) milk loss estimates based on discarded milk only. The common assumption of
the methods of Chapter 3 and other cost of disease estimates (Janzen, 1970; Natzke, 1976;
Fetrow eLel, 1987; Goodger and Skirrow, 1986) seems to be that the total of expenses
associated with the occurrence of disease represents the true cost of the presence of that
disease. The underlying premise is that a disease free alternative exists, and that the
elimination of disease will result in an increase in profit equal to the total of expenses.
These methods overlook savings due to disease and the effects of changes in population
structure, due to disease that may effect the total economic picture. Also, since a disease
free utopia is unlikely, it would be more appropriate, for the individual farm manager,
to consider the economic impact of changes in disease level or management strategies
that affect disease, versus the cost of disease.

The objectives of this chapter are 1) to apply the epidemiologic simulation model
of Chapter 7 to economic analysis of Clinical Respiratory disease, 2) define and estimate
the cost of respiratory disease in an "average" Michigan dairy herd, and 3) to determine

the effects of changes in the level of various management characteristics on this cost.

117

118

MATERIALS AND METHODS

The epidemiologic model for simulation of a dairy herd has been described in
Chapter 7. A subroutine was added to this model to compute dairy income and disease
influenced variable costs. Revenue and expenses are computed on the basis of the
number of individuals in any given disease state, in addition to animals sold. The block
diagram for computation of dairy income and disease influenced variable costs for all
animals not in the CLINICAL state is shown in Figure 81 a,b. This was implemented
in order to include the economic effects of changes in population structure due to
disease, but not directly observed as disease expenses. The costs and income generated
by this portion of the model will differ as the level of disease in a herd changes.
Income, costs, and disease associated expenses directly related to disease are computed
according to Figure 8.2.

The sum of costs generated in Figures 8.1 and 8.2 are termed the Diseased
Influenced Variable Costs. The Diseased Influenced Variable Costs include feed costs
for Calves, Young Stock, and Cows, purchasing costs for replacement of Cows, variable
costs of milk production, and disease associated expenses. Disease associated expenses
were estimated from the NAHMS database and include veterinary fees, drugs
administered, and labor for care and treatment (Figure 8.2) Variable costs of milk
production include items such as hauling and advertising. Building depreciation,
equipment repairs, and interest are not included in the analysis as they do not change
with the frequency of disease. The tax effects of selling livestock was not addressed.
Purchasing costs were modelled for Cows only. This was implemented by an inventory
control routine that would initiate the purchase of cows, at a set price (Table 8.1), if the
inventory, of cows, dropped below the starting level.

Feed costs, for all disease states, were modelled by assigning a daily intake rate,
per head per day. Daily intakes and price per pound of feed (Table 81) were estimated
from NRC (1987) recommendations and application of the Spartan ration balancer

(MSU/CBS, 1987) to generate a typical ration for each age of animal. It was assumed

119

 

 

 

Table 81 Economic parameters for the "average" dairy herd
Variable Default Units Comments Source
CALEB
Fannie birth rate 0.43 hdlcowlyr ABC 508
Male birth rate 0.43 bd/cowlyr Sold at birth ABC 508
Purchase rate 0
Poordoerrate 10 % fiofpaninfectedthat
perform poorly
Cull value-non—resp 120 S/hd A-nne these are same value ABC 508
as bulls
Cull value-poor doer 100 Slhd Asume 20% reduction in value
Bull calf value 120 Slhd ABC 508
Drug Tx Expense 0.5 Slcase/day Data
Labor Tx hours 0.33 hr/caselday Data
Vet Tx Expense 0.05 S/case/day Data
Daily haste-non Cx 4 I feed/day For 165 pound calf NRC
Daily intake-poor 3.5 I feed/day 24% decrease with in gain, Miller, 1980
no change in feed conver-
sion ratio
Daily imake-Cx 2 l feed/day Maintemnee only
Price feed 0.05 SI! .07 SI! for milk replacer, Data
.04 SI! for dry feed
Diacardmilktocalves 50 % fiofmilkdiseardeddueto Data
amibiotic treatment that
is fed to calves
YOUNG STOCK
Poordoerrate l % iofpastinfeetedthat Bloodand
perform P00“! Henderson,
1985
Cull/sell vahIe-non-resp 1000 Slhd Assume sold for dairy
Cull value-poordoer 260 Slhd Assume20% decrease invalue
Drug Tx expense 0.47 Slcaselday $3.28/case for 7 days Data
Labor 1'): hours 0.034 hr/caselday .23 hr/ease for 7 days Data

Table 81 (cont’d.)

120

 

 

Vet Tx expense 0.03 SIcaseIdsy $.21Icsse for 7 days Data
Daily imake-non-Cx 16 I feed/day Average lZ-month-old heifer NRC, 1989
at 660 lbs
Daily inake-poor 14 I feed/days 2-7% decrease in decrease Miller, [980
daily still
Daily imake-Cx 8 I feed/day Maintenance only
Price feed 0.03 S/I 4I and shell corn, 12I MSU/CBS, 1987
alfalfa grass hay, 7I corn
silage with vitamin premixes
COWS
Milk production-non—Cx 41.7 Ilday Based on l5,000 I for 360 days
Milk production-C11 10 IIday
Milk price 12 Slcwt
Poordoerrate 0 % Sofpastinfectedthatperform
poorly amme no effect in adults
Purchase price 1500 Slhd Price of replacement cow
Cull value-non-resp 546 SM 1300I 0 $.42” ABC 508
Drug Tx expense 1.8 $Icase/day $l3lcaae for 7 days Data
Labor Tx hours 0.08 S/caselday .5Icase for 7 days Data
Vet 'l‘x expeue 0.75 SIcaseIday 5.30Icase for 7 days Data
Daily Make-maintenance 24 DM IIday Based on feeding 60-month- MSU/CBS, 1987
old dry cow
Daily illakeII milk 0.3 DM III milk MSU/CBS, 1987
Variable cost of milk .Ol/I 3" milk For advertising
hauling, etc. ABC 508
Discard milk 50% % Assume 50% of sick cows are treated
Price feed 0.03 SII MSU/CBS, 1987
ALL AGES
Discoum rate 0.1 %Iyr Opportunity cost of iner-
mediste term capital
Wage rate 5.5 S/hr ABC 508
Infection duration 7 days Average time in CLINICAL Literature
ImnItnity durauon 360 days After natural infection
Vaccination duration 270 days

 

121

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2.59 sue-v. 2:...» :38 1:!

 

 

 

 

 

 

 

 

 

   
                

 

 

 

ans-u Inna»

 

 

 

       

€13. «...-n

:3. out;

 

 

 

3.....1
coon cos; d.»
.33. ...-up .2.- ..au
:3. out; .0..— can. .4 t
N + 5“ in
(Fla .
no... van.
:0... can;

 

2.2a. 1.2

 

 

 

on.“ has.»
...-.... we...

IDs-.00.: I
DESI-lu—

 

 

...-8
can.»
123.99..

 

 

no.8
can.»
49...:

 

 

 

   

2a:
:0... .35

..au of 03¢ a...
.00; :09

     

.3
out; I...

        

 

 

 

 

 

  
  

.03-u 0. to.

.=' mb-u-I-mu

...->5?»
...—Inabznufi in!

338
...-ll.

 

 

, 3......
ie.-3.3.-

 

 

3......
a“. to:

 

 

 

Dairy income and Disease influenced variables cost for CALVES and
Young Stock. Block diagram

Figure 81a

122

  

.309 .....o ....

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

13.12.:
”’09
E
....u .....u 2... 3a.
...-.... ...... I...

EDD-I ‘

 

 

 

 

 

 

 

 

 

2....
5...:

 

 

 

 

 

 

1
I... I... a... six.
. l ....
al‘x‘le ...... ....
not...
...-93‘...— J...

Dairy income and disease influenced variable cost for COWS

Figure 81b

E.- .. ... ...-....

.81.... a... .83....
» .... .s8... ...:
a a e
34...... ...
...... a... .... .... 8
0 ...l....— ... 2... .... n.“ "...-”nunu .39....“ ...—“Ha

     
   

...... n

+ ...-.5 ...-...
... 5......
...... ....

......- a...

    

 

   

 

 

 

 

 
   

  

 

fiaixg
2......— E 32...... a ...-......l
0. ... ...-... .... ....- .. u.
«I...
....u H a e + + .33...
. ... 5...... :3 +
+
.23...
5.3.2.... ....-
..s... a...
a 28.3.... p L ....s .. a.

 

 

no... ....»

 

 

 

=2 .
“......” .... a +0 T + .. ...—....

 

 

 

 

 

 

 

Computation of expenses associated with CLINICAL disease

 

 

   

 

   

 

 

+ + + +
g g .13: _o a.
...—...
...... ,
8:86.... ... a h .02-=9
Ex».
....
...!
5...... A 53...... —..!....5.1_
3...... ... ...-.... .... ...-...... ... a... 3...... ...

 

 

 

Figure 8.2

124

that the average animal in the healthy calf population weighed 165 lbs (75 kg) and
should be eating approximately 4 lbs. of dry matter per day. A ration of corn, soybean
meal, midbloom alfalfa and trace minerals salts costs 804 per pound with current prices,
1987 in Michigan, from the ration balancer. Some of the feed given to Calves includes
milk replacer priced at 8.07 per pound reconstituted, so the average price was set at $.05.
The total amount of daily feed for Calves was reduced by 50% of the amount of milk
discarded due to antibiotic treatment of cows. This feedback feature allowed the effect
of disease and antibiotic treatment in Cows to decrease the cost of feeding Calves.
According to the NAHMS data (Chapter 5) it was estimated that 50% of antibiotic
tainted milk is fed to Calves. The average Young Stock was assumed to be 12 months
old and weigh 660 lbs (300 kg). These animals consume 16 lbs (7.3 kg) of dry matter per
day at a price 3.03 per pound. For adult Cows, a ration was formulated for a 1300 pound
(590 kg) body weight dry cow to determine the daily maintenance intake. Intake per
pound of milk was estimated from rations developed for a cow making 60 and 20 pounds
of milk per day. The average price for a ration of corn silage, alfalfa hay, ground shell
corn, and soybean meal, with minerals was 803 per pound of dry matter (Table 81)

For Calves and Young Stock in the CLINICAL state, it was assumed that there
was a 50% decrease in daily feed intake. For poor doers (Chapter 7), a 10% decrease in
feed intake was estimated from Miller m], (1980), since it was stated that growth
decreases, without a decrease in feed conversion. Cows in the CLINICAL state
produced only 10 pounds (4.5 kg) of milk. For Cows, it was assumed that the decrease
in feed consumption was reflected in the decrease in milk production.

The computation of expenses directly related to disease is shown in Figure 82.
As disease progresses in a herd, according to the processes described in Chapter 7, the
CLINICAL states will fill with animals then drug, veterinary and labor expenses will
begin to accrue. Sick animals will still generate some revenue, Cows still milk and
Calves and Young Stock will still be sold. Acutely ill Cows will milk at a decreased
rate. Also, feed intake, in all age groups, will be decreased during illness so that some

savings will occur.

125

A portion of Young Stock and Calves, that have been diseased, will have chronic
effects that decrease their growth rate. The animals are often called "poor doers" and
the portion is the poor doer rate (Table 81). The poor doer rate only applies to animals
in the IMMUNE and RECOVERED states. However, Calves that are born into the
COLOSTRUM IMMUNE state are not affected. It is assumed that cows in the
IMMUNE state carry no residual effects of disease. This assumption is based on the
clinical experience, and the observation of no respiratory related cull in the NAHMS
database (Table 81).

Income was generated by animals in all states of disease. Income was derived
from the sale of milk and sale of animals. Fifty percent of the Calves born were sold
as veal Calves. Heifer from the Young Stock age group were sold if the inventory of
heifers exceeding the original numbers. This maintained a constant herd size and helped
to account for the effects of disease on animal populations. Culling rates in cows for
non-respiratory disease were estimated from the NAHMS data (Table 81).

Milk production was defined as an average 15,000 pounds (6818 kg) per lactation,
at the beginning of the run, for Cows that were not in the CLINICAL state. Milk
production increased annually as a function of the rate of new heifers freshening into
the herd, in order to include the long term effects of genetic improvement. An equation
was defined so that if 30% of the milking herd was replaced in one year, then the daily
milk production parameter would increase by 2% (Radostits and Blood, 1985, pp 196-
200). Milk price was set at $12 per hundred weight.

The difference of Gross Income Dairy and total Diseased Influenced Variable
Costs, was computed every 30 days. The Net Present Value (NPV) of this monthly
stream of income was discounted (Barry, gel, 1983, 206) back to the beginning of the run.
This procedure served to equalize differences in the timing of disease occurrence from
one scenario to another. Therefore, an epidemic that occurred in Year 1 of a run could

be compared to an epidemic that occurred in Year 5, for example.

l l I l 3 l. .
The parameters of the simulation herd were set to define an "average" Michigan
dairy herd (Table 8.1). This herd had 11 Calves in the herd, 41 Young Stock, and 81 cows.
This is equivalent to the NAHMS Stratum II herd (Chapter 1). The Cows were 1300
pound (590 kg) Holsteins, milking 15,000 pounds (6818 kg) per year. The disease free herd
(BASELINE) was simulated for a 5 year period by setting the initial annual Incidence
density and Secondary attack rates near zero, since division by zero in the computer
program produced an error. The probability of a new infection was set to zero. An
initial infective was added at the beginning of the run, in order to provide disease
expense comparison to disease runs that also started with one initial infective. This
disease free herd served as the standard of comparison by which the Cost of Respiratory
disease could be computed. The Cost of Respiratory disease was defined as the
difference in 5 year NPV for the disease free herd compared to the diseased herd.

Diseased herds were computed in various manners to represent the different
possibilities that might occur. Diseased herd #1 (DISEASE 1) was run with the average
annual incidence densities (aID’s), probability of new infection (ProbNew), and
Secondary Attack Rates (SAR) set at the mean values observed in the data (Chapter 5,7).
All animals were considered susceptible at the beginning of the run.

DISEASE 2 might represent the "average” DISEASE 1 herd that now adds the
risk factor OHIREPOS (greater than 50% of non milking labor is hired help).
According to the logistic model of Chapter 5, the addition of this factor should increase
the probability of disease (odds) 2.8 times in Calves and 1.8 times in Cows. The initial
aID’s and SAR’S were adjusted accordingly. In DISEASE runs 3 and 4, the SARS were
set at twice the average and 2 infectives were added to the initial population, to
stimulate high disease rates. In DISEASE 4, the Case Fatality rate was set at a high
level (50%) in all age groups in order to estimate the cost of an extremely pathogenic

disease.

127

RESULTS
Model parameter settings and results are shown in Table 82. The high disease
herds, DISEASE 3, DISEASE 4, both experienced the same distribution of case numbers.

The bimodal frequency distribution is shown in Figure 83.

DISCUSSION

This model allows for improved estimates of the costs of respiratory disease as
it includes feed savings and increased income from animal sales due to illness. The
representation of the bimodal stochastic behavior of disease occurrence allows for
estimation confidence intervals on the NPV. The effect of disease frequencies higher
than the ”average” reflected substantial costs.

The costs of respiratory disease reported in Chapter 3, would predict, $14 per
calf/year, $1.95 per heifer/year, and $1 per cow per year, for the average frequency of
disease observed in the whole sample. Given the average herd size simulated, the 5 year
total expected is approximately $1,490. This should be compared to model output for
DISEASE 1. However this simulation represents only one particular herd type, Stratum
II. A more detailed within stratum comparison is indicated in order to make judgments.
It is possible to generally conclude, as noted in Chapter 3, that the standard NAHMS
procedures for cost estimation need to be adjusted for changes in the overall economic

picture of the herd.

SUMMARY

The ability of the model to facilitate economic analysis of different disease
scenarios and configurations has been demonstrated. Application of this model with
stratum specific parameters and sample characteristics should allow for improved
estimation of the cost of respiratory disease in Michigan. The application of different

parameters should also allow for estimation for other diseases.

128

Table8.2 Shudadonmdbfor'avemge'hfichigmdairyhcrdfithdiflemmbvehofdiaeaudyearruns.

 

 

Milk
and Cost
Age Initial feed Purchase Animal Milk 5 yr. of
Group 113(0) SAR infectives costs cost sales Sales NPV disease
Baseline
A 0 0 0 176,530 30,529 108,061 873,395 756,405 0
B 0 0 0
C 0 0 0
DISEASE!
A .03 .106 0 154,690 28,873 91,704 726,672 634,685 121,720
B .(X)5 .019 0
C .002 .005 0
DISBA8B2
A .08 .3 0 154,839 34,207 93,469 726,130 630,419 125,986
B .005 .019 0
C .0034 .01 0
DISEASB3
A .(B .2 2 149,365 34,165 89,011 708,122 613,339 143,066
B .005 .04 2
C .002 .01 2
DISEASB4
A .03 .2 2 125,425 54,371 92,273 706,102 595,963 160,442
B .005 .04 2
C .002 .01 2

 

Initialgroupsize: calves(A)-11,youngstock(B)=4l,cows(C)-8l

 

 

Frequency Distribution of Number oi Cases
oi Respiratory Disease per year
for Disease Scenario'. 3
Calves

 

I Observation.

BSBSS

*
O

 

 

 

4 1

O

0.0-2.0 2.1-4.0 4.1-5.0 5.1-0.0 8.1
Mas-sperm

 

 

128

 

 

Frequency Distribution of Number of Cases
of Respiratory Disease per year
for Disease Scenario: 3
Young Stock

 

\l
o

0 Observation.
8 8 6 8 8

£5

 

 

 

..L

10.1-15.0 20.1-25.0 30.1-35.0
15.1-20.0 25.1-30.0 35.1-40.0
”drawn“

0

0.0- 5.0
5.1 -10.0

 

 

Frequency Distribution oi Number of Cases
of Respiratory Disease per year
for Disease Scenario 3

Cows

 

fl Observations

315388383

 

 

Figure 83

 

 

 

A — A L A. I I
r f V

0.0-10.0 20.1-30.0 40.1-50.0 60.1-70.0
10.1-20.0 30.1-40.0 50.1-60.0 70.1-80.0

 

 

lCosesperyaor

 

Bimodal distribution of number of cases from DISEASE3

SUMMARY AND CONCLUSIONS

This dissertation is directed toward the development of methodologies in
analytical epidemiology and animal health economics. The system to which these
methods were applied is the National Animal Health Monitoring System, and disease
frequency and cost estimation in Michigan dairy cattle. Stratified random sampling of
dairy herds, with prospective observation of one year was implemented. Methodological
issues in the computation of disease frequencies and their variance were addressed and
a standard method proposed. Issues relating to the estimation of the costs of disease
were discussed, and shortcomings in the standard N AHMS methods noted.

Simulation modelling in epidemiology was reviewed for the purpose of evaluating
alternative modelling strategies to be implemented in the context of NAHMS. A
comprehensive classification scheme for epidemiologic simulation models was proposed.

A risk assessment analysis was performed using associative epidemiological
models, and the utility of NAHMS for this purpose was discussed. Estimates of the
effects of various risk factors on the occurrence of Clinical Respiratory Disease were
to be incorporated into the simulation models of Chapter 7 and 8. This was
accomplished only modestly, due to imprecision in the analysis due to small sample size
and time frame incompatibilities between the simulation model and statistical model.

The distributed delay approach was proposed as a generic subunit to be used in
a variety of infectious and non-infectious disease models. The model was applied, by
way of example to Clinical Respiratory disease in dairy cattle. The model was to
approximately predict the observed annual incidence density for example herds from
the database. Many specifics about the herds were not available to the model, which
decreased its precision. The simulation model was a useful tool for evaluating the long
term economic impact of disease on the farms gross margin of Dairy Income minus
Disease Influenced Variable costs. Many different scenarios could be evaluated with
this model. It may also be useful as a statistical estimation tool to determine the "true"

cost of disease in a population.

129

APPENDICES

APPENDIX A

Data collection forms for Michigan Round I, N AHMS

Producer Code No.

FORM 1 - Dairy
Initial Visit
National Animal Health Monitoring System

VMO code

_=e9_=_

Interview date:__[__/

 

 

 

 

 

 

 

 

yr mo day
1. Milking herd replacements Raised % Purchased %
No milking herd; only raises replacements
2. Facilities (check appropriate items)
HOUSING Calves Young Lactating Dry
Stoc Cows Cows
Stanchion barn
Loose housing
Free stall housing
Dry lot
Pasture (in season)
Individual calving stalls
Calf hutches
Calves in cow barn
Separate calf barn
Milking parlor used Type of parlor
3. Farm activities: Dairy breed used 1 %
Other livestock enterprise(s)
Major dairy ration components (check appropriate items)
,— % Raised % Purchased
May, alfalfa or other legume
Key, grass
Silage, corn
Silage, other
Other major feeds fed
(speélfyli
4. What disease problems of significance occurred in your herd during the past
2 years?
5. Use of veterinary or other service:
Veterinary service is used times per month or times per year.
Nutritional consultant is used yes no
Type of veterinary service obtained (check all that apply)
Treatment of sick livestock Herd health Source of vaccines
Disease investigation General advice Other (specify)
6. Comments? (if yes, check here ) Please use reverse side of page.

130

131

FORM 1 page 2 - Dairy
Initial Visit
National Animal Disease Surveillance
** Print with black pen or type *a

State Co. Sp. Herd
Producer Code No. VMO code Report month

 

 

 

7. Reproductive services: (check all that apply)
Pregnancy exams Problem Breeders
Post-partum on all cows Prebreeding on all cows

8. Type of nutritional consultation received
Analysis of major feeds (yes or no) How often (per year)
Customized ration formulation based on analysis (yes or no)
Milk cows , Dry cows , Young stock
Adjustment of feed intake according to production level (yes or no)
Grain only , Grain and forages

9. Nutritional consultant

Commercial feed rep , Local teed mill , Extension service
Private consultant , Veterinarian

10. Record system (check all that apply):
No systematic record system
Reproductive events present lactation only
Reproductive events for cows entire life
Complete history for entire life (all pertinent events recorded)
Milk production record for present laction only
Milk production for entire milking lite
DRIA Permission to access, no yes (please sign below)
DIIIA code O
Other form of production records

 

 

 

AGREEMENT

The undersigned does hereby warrant ownership and control of a certain herd of
dairy cattle, and gives permission to the Dairy Herd Improvement Association
(DMIA) to allow NADDS of Michigan to examine the herd's production and somatic
cell count records with the provision the records will remain confidential bet-
ween DMIA, NADDS and no reference by either name or herd number will be per-
mitted, published or otherwise released to the general public at any time.
However, the material referred to may be used and otherwise utilized for scien-
tific purposes, including publication, provided said herd's identity is pro-
tected from public disclosure. Your cooperation is completely voluntary, with
no penalty for declining to participate.

Signature Date

 

132

FOR! 2 - DAIRY

Monthly Inventory and Producer Cost Report
National Animal Health Mcnittring System

**Print Clearly with Pent.
Producer Code: 22 : : 20 : VMO: Interview Date: 1 a
Report for the Month of

 

CATTLE INVENTORY:
A) Calves ( birth to weaning )

Last Month + Live Born + Q Bought - 3 Sold - i Weaned - 9 Died - t at_§gg

+ + - - - -

 

B) Young Stock ( weaned to first calving )
Newly 9 0 Sold Disease Non-Dis. 3 #
Last Mon + Weaned + Bought - Dairy - Culled - Culled - Calved - Died 3 t at End

+ + - - - - - -

.-

 

 

 

 

C) Cows ( all cows & heifers that have calved )
lst.Cal£ # Sold Non-Dis. C.sease
Last Mon + Heifers + t Bought - Daigy - Culled - Culled - 9 Died - 9 at End

+ '0' - — - - I

 

D) Bulls ( for breeding purposes )
EM+LM'L&1§-L£EAE'LQJEQ -#at£nd

+ " - - -

PRODUCER COSTS OF DOING BUSINESS:

 

 

 

 

 

 

 

Itgg 5 Cost Hours ot_gg§9r
Veterinary Consultation S ____ hours
Milking Machine Maintenance 45‘. hours
Other: 5 hours

 

 

 

(DO NOT include teat dip,etc)

£11k Sold: ~pounds. at S / cwt ( net price )

Somatic Cell Count/Score: from: 0513 upr wnm Other:

( circle one, please )
Bacteria Count:

 

tired Labor Wage Rate: 5 / hour
{umber of Form 3s Submitted this-month:

’roducer Code:

133

FORM 2A - DAIRY

Monthly Preventive Mess

ure Report

National Animal Health Monitoring System

22 :

Report for the Month or

**Print Clearly with Pen**

: 20 : VMO:

 

 

iULK PURCHASES OF PREVENTIVE MEASURES:

Disease/
tondition

 

Vaccine or Drug

 

Purchase Cost(§)

 

 

Interview Date: 1 g

EKQQCted : Head to Treat

 

 

 

 

 

 

i“ in 1w Lm -m

 

 

 

 

’REVENTIVE MEASURES ADMINISTERED THIS MONTH:

 

 

 

 

 

MO Groupir

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Vaccine,
-isease / Drug, or
:mmmmueee
_L‘
_3, ______
5
_§ ._____.
i _—
i ....—
_§
_§_
_§
_ 3
_§,
_§,

 

* - Age Groups 2 A)Calve

lllllllll

 

 

s, ”Young S

O.9.........OOOOOOOOOCOOOOOO0..........0...... .........

Labor Hrs
hr

hr

hr

hr

I.

hr

L

hr
hr

1.

I.

I.

hr

l

hr
hr

 

 

hrs

 

hrs

I

I

§——' .—

tock, C)Cowm, D)Bulls

PORN 3 - DAIRY

Monthly Disease Cost Report
National Animal Health Monitoring System

nPrint Clearly with Pent.

Producer Code: 2 : : 20 : VMO: Interview Date: 1 1
Report for the Month of

 

1) Disease or Condition:

 

Describe signs observed and affected body parts:

 

 

2) Diagnosis affirmed by ( check all that apply ):
Owner/Operator VMO Private Practicioner Lab

Other ( please specify ):

 

3) Age Affected: A)Calves B)Young Stock C)Cows D)Bulls B)CalVes born Dead
( circle one. please )

4) NUMBER OF CASES, AND COSTS INCURRED:
a) i Cases from Last Month:
b) 9 New Cases This Month: +
c) 8 Cases Recovered: -

d) 0 Cases which Died of this disease: - Loss of §

 

e) I Cases Culled for this disease: - Loss of S
f) Total Number of Cases at End of Month:
9) Weight Loss lbs. Loss of §
h) Veterinary Service: §
1) Vet supervised Drugs: § Owner Discretion Drugs: 5
1) Cost of Carcass Disposal: - §
k) Hours of Labor for Treatment: hrs
1) number of Calves born Dead: Loss of g for calf(s)
m) Pounds of Milk Discarded: lbs Production Loss lbs

 

List Drugs Used below ( please try to rank according to frequency of use )

l l L

1 l J

135

Iktienal Animal Disease Surveillance

Product’s Daily Birth, Death and Disease Log

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Month Year
mi of Cow Record new Disease ‘ '
or or Condition or Mo. we. Vet Drug Labor Milk
:lass of Calving date (calf- Animals Treatment Loss' Costs Costs .Bours Loss
Cattle Live/Deed) or deaths Affected Given lbs. 3 3 lbs.
1
‘Ou‘W,~.M" -' mama-..wm‘wem "w. . or”... .01.!" -~- any . - v.1. -

 

136

 

 

APPENDIX B
Table 8.1 Disease groupings used in NAHMS in Michigan in round I, 1986/87.
Group Composition
Gastrointestinal Bloat, coccidiosis, constipation, displaced abomasum, diarrhea,
enteritis, entcrotoxemia, hardware, indigestion, intestinal
obstruction, intestinal hemorrhage, intestinal infections,
pneumoenteritis, polyphagia, ulcers, actinomycosis
Respiratory Pneumonia, respiratory problems NOS“
Lameness Lameness, foot rot, corns

Metabolic/nutritional

Mastitis

Breeding problems

Birth problems

Multiple system

Integumental

Urogenital system

Acidosis, downer cow syndrome, ketosis, low magnesium, milk
fever, nutritional deficiency, overweight, polyphagia, selenium
deficiency, vitamin E deficiency, white muscle disease

Clinical mastitis, septic mastitis, toxic mastitis

Anestrus, cystic ovaries, follicular cysts, false pregnancy,
metritis, pyometra, repeat breeder, reproductive problems N 08",
vaginitis

Abortion, dystocia, prolapsed uterus, retained placenta, uterine
torsion, vaginal tears

Abscesses, accidents, agalactia, allergies, encephalitis, fever,
infections NOS, injuries NOS, handling injuries, tail injuries,
lethargy, no milk letdown, malignant lymphoma, navel ill,
neonatal death NOS, neoplasm, disease NOS, off feed, peritonitis,
poisoning, poor condition, umbilical hernia, weakness, weight
oss

External parasites, fungal skin infections, hematomas, mycotic
dermatitis

Nephritis, urinary tract infections NOS

 

*NOS = not otherwise specified.

APPENDIX C
Quick Basic programs for stochatic epidemic simulation

DECLARE SUB EXPON (MEANI, XVAR!)
DECLARE SUB TRIDIS (Al, 3!, C1, VALCUR!)
DECLARE SUB DELLVFS (RINI, ROUTI, ST!(), STRGl, PLR!, DEL1, DTl, K!)

’OOOOOOOOOOOOOOOOOOOOOOOOOOO.....OOOCOOttttttt......OOOOCOOOOOOOOO

'- PROGRAM DDDBIT - DISEASE USING DISTRIBUTED DELAY - 5/16/89
"...OOOOOOOOOOOOQO.....OOQOOOOOOOOOOOOOOODOOOOODOOOOOOOQO..00....

'* THIS PROGRAM MODELS DISEASE AND OTHER PRESSURES ON POPULATION
': (ROUTINE CULI..S, GROSS MORTALITY). THE DISEASE PROCESSES

'- (INFECTION AND RECOVERY) ARE MODELLED USING DISTRIBUTED DELAYS
w ADJUSTED FOR POPULATIONS AND PREVIOUS LEVELS OF INFECTION
’OODOOODOOOO........ttltttltOOOOIOOQOOit‘t.......Olltttttttttttttt

'- VARIABLE DICTIONARY (ALPHABETIZED) "

’OOOODOO VARIABLES SET BY USER OOOOIOOCOOOOOO

'- BETAMAX : MAXIMUM VALUE THAT BETA CAN ASSUME

.. BETAMIN : MINIMUM VALUE THAT BETA CAN ASSUME

" IDT% : NUMBER OF DIVISIONS OF T FOR CALCULATIONS (I/DT)

"1 INFDUR% : NUMBER OF DAYS INFECTION LASTS (DURATION)

’: KI :NUMBER OF STAGES FOR INFECTED POPULATION

'* KN :NUMBER OF STAGES FOR NONINFECTED POPULATION

"1 MREPRO : MEAN DISEASE REPRODUCTIVE INDEX

w NDAYS% : NUMBER OF DAYS IN A RUN

1: NRUNS% : NUMBER OF RUNS TO PERFORM

"1 OPPN (2) : ORIGINAL POPULATION LEVELS:

': 1: NONINFECTED; 2: INFECTED

'r PRDAY% : PRINT DAILY DATA FLAG ( 0 = NO, 1 = YES )

'r STOC% : DON’T RUN STOCHASTICALLY FLAG ( O = RANDOM, I = NOT)
’ODOOOOOOO VARIABLES SET DURING RUN OOOOOOODOI

.. ATTRAT : ATTACK RATE

’* SUMATRT : SUM OF ATTACK RATES FOR AVERAGE CALCULATION

’r BETA : INFECTION CONTROL PARAMETER

': DEL : CURRENT DELAY FOR DELAY ROUTINES

"' DT : DIVISION OF DAY 1 / IDT%
" ID (2) : INCIDENCE DENSITY CALCULATION COMPONENTS
"' 1: NEW CASES; 2: NUMBER AT RISK

" INFDEL : DELAY FOR INFECI‘ING PROCESS
" INFOUT : RATE OF RECOVERY
"' PLROUT (2,2) : PROPORTIONAL LOSSES BASED ON AGE AND TYPE OF LOSS

" (A,B): A = 1: CULLING; 2: DEATH (LOSSES)

" B = 1: NONINFECI'ED; 2: INFECTED

"' PLRRTE (2): PROPORTIONAL LOSS RATES:

" 1: CULLING; 2: DEATH (LOSSES)

" PPN (2) : POPULATION LEVELS ADJUSTED THROUGH RUN (SEE OPPN)
" 1: NONINFECI'ED; 2: INFECTED

" SINF (KI): STORAGES FOR KI STAGES OF INFECTEDS

" RINI : ADDITIONS TO POPULATION USED IN INFECTION DELAY

"' RINN : ADDITIONS TO POPULATION USED IN NONINFECTED DELAY
" SNON (KN): STORAGES FOR KN STAGES OF NONINFECTEDS

137

138

” RSUM (2): SUM OF TRANSFERS OF ANIMALS:
" 1: SUM OF INFEC'IEDS; 2: SUM OF RECOVERIES
” SHFF% : EPIDEMIC SHUTOFF FLAG ( O: NO, 1: YES )
" STRG (2) : STORAGE FROM DELAYS: 1: NEW DISEASED; 2: NEW RECOVERIES
" WELOUT : RATES OF INFECTION
't000‘.....O...ODOOOOOOUOOOOOCDOCCOCttttttttttttttttOtttttttttt.......
" PREPARE FOR RUN
CLEAR
INPUT 'Would you like hard—copy output? ( 1 = Yes, 0 = No ): "; 1%
IF 1% = 1 THEN
P5 = 'LPle'
ELSE
P5 = 'SCRN:" here-«-
END IF
OPEN PS FOR OUTPUT AS #2
INPUT "Write Histogram to 1: Screen, 2: Printer, or 3: File - "; 1%
IF 1% = 1 THEN P8 = 'SCRNz'
IF 1% = 2 THEN P5 = 'LPle'
IF 1% = 3 THEN INPUT "Enter File Name: '; PS
OPEN PS FOR OUTPUT AS #3

re
’##.#OOOOOO$8.11.0000000IOOOOOOCOODOQOOCt*¥#¥*¥##ttttt$tfittttttltfitfiil
’* INITIALIZE ARRAYS
9e

DIM ID(2), oppn(2), PLROUT(2, 2), PLRRTE(2), ppn(2), RSUM(2)

DIM STRG(2), BAR(3, 20)

’OOOOOOOOOOOOOOUOOOOOOOOOODOOOOOOOOO.it.OOOOOOOOOOIOOOOOOOIOOOCOIt.ttt

"' PROMPT USER FOR INPUT
vs
INPUT "Enter number of stages in noninfected delay: '; KN
DIM SNON(KN)
INPUT ”Enter number of stages in infected delay: '; KI
DIM SINF(KI)

9e

’"” INPUT POPULATION PARAMETERS
ts
100 INPUT “Enter number of UNINFECTED cases to start with: '; oppn(1)
INPUT “Enter number of INFECTED cases to start with: "; oppn(2)
’"" INPUT DISEASE PARAMETERS
re
INPUT “Enter number of days infection lasts per case: ', INFDUR%
' INPUT 'Enter Mean Disease Reproduction Index: ', MREPRO
INPUT ”Enter mean BETA for the distribution;", BETA
’“" INPUT SIMULATION PARAMETERS
9e
INPUT “Enter number of runs you wish to perform", NRUNS%
INPUT "Enter number of days to run simulation for:', NDAYS%
INPUT ”Enter number of divisions within each day (1/dT):", IDT%
DT = l! / IDT%
INPUT “Run with random variation? ( 1 = Yes, 0 = NO ):", ST%
IF ST% = 1 THEN
INPUT “Type of distribution: 1 = Triangular, 2 = Standard:"; STOC%
’ INPUT "Enter minimum value that Beta can assume: '; BETAMIN

139

’ INPUT ”Enter maximum value that Beta can assume: "; BETAMAX
RANDOMIZE TIMER
ELSE
STOC% = 0
END IF
SUMATRT = O!
SUBR% = INT((oppn(1) / 20) + .5)
MIN = 0!
MAX = SUBR%
FOR I = 1 TO 20
BAR(1, I) = MIN
MIN = MAX + l
BAR(2, I) = MAX
MAX = MAX + SUBR%
BAR(3, I) = 0!
NEXT I

’ttttttttIOttttttttlilttttiltttttttt01*ttflfitit¢tttttfitttttt¢tlIt!!!

"m BEGIN RUNS ""-

re

FOR R = 1 TO NRUNS%
ve
"' IF MULTIPLE RUNS, PRODUCE A HEADER
PRINT #2,
IF NRUNS% > 1 THEN PRINT #2, "Run # '; R
’ INITIALIZE ARRAYS AND VARIABLES AT BEGINNING OF EACH RUN
FOR B = 1 TO 2

PPn(B) = OPPH(B)

STRG(B) = 01
ID(B) = 01
RSUM(B) = 01

FOR C = 1 TO 2
PLROUT(C, B) = 01
NEXT C
NEXT B

’ BETA = MREPRO / (ppn(l) " INFDUR%)
infdel = (I! / (1! - (1! - BETA) " ppn(2)))
"' INITTALIZE STORAGES FOR DELAY ROUTINE CALLS: UN INFECTED AND
INFECTED
FOR I = 1 TO KN
SNON(I) = ppn(l) / KN
NEXT I
FOR I = 1 TO KI
SINF(I) = ppn(2) / K1
NEXT I
welout = O
INFOUT = O
shff% = O
"" SET DELAYS TO INITIAL VALUES ’
DEL = INFDUR%
idel = infdel
’"* GENERATE PLR- PROPORTTONAL LOSS RATE (CULL AND DEATH RATES)

1e

PLR = PLRRTE(I) + PLRRTE(2)

140

’“" LOOP FOR DAYS ""‘
9.
FOR D = 1 TO NDAYS%
"” FIRST, CHECK TO SEE IF THE POPULATIONS ARE STILL THERE (SINCE THERE
ARE NO INPUTS) - IF ALL THE ANIMALS ARE GONE, END THE RUN
’t
IF ppn(l) <= 0! OR ppn(Z) <= 0! GOTO 900
’"" LOOP FOR DIVISIONS WITHIN DAY ”’"
FOR T = 1 TO IDT%
’0
”" CALCULATE PLR LOSSES : THIS CAPTURES LOSS FOR EACH TYPE OF
PROCESS
" (THE DELAY ROUTINE DOES NOT FIGURE THESE SEPARATELY
FOR C = 1 TO 2
FOR I = 1 TO KN
PLROUT(C, 1) = PLROUT(C, 1) + (ppn(l) ‘ PLRRTE(C) / idel) ‘ DT
NEXT 1
9e
"" IF THE EPIDEMIC IS OFF, INCLUDE THE ANIMALS THAT WOULD HAVE BEEN
INFECTED
re
IF shff% THEN
PLROUT(C, 1) = PLROUT(C, 1) + (welout * PLRRTE(C)) ‘ DT
END IF
NEXT C
"" CALCULATE PLR LOSSES FOR INFECTED POPULATION
FOR I = 1 TO KI
FOR C = 1 TO 2
PLROUT(C, 2) = PLROUT(C, 2) + (ppn(2) ‘ PLRRTE(C) / DEL) ‘ DT
NEXT C
NEXT I
re
’"" MODIFY PARAMETERS FOR RECOVERY DELAY
"" GENERATE RINI - ADDITIONS TO INFECTED POPULATION. IF EPIDEMIC IS
OFF, DO NOT ADD NEW CASES FROM THE INFECTING DELAY
9.

IF shfl% = 0 THEN
RINI = welout
ELSE
RINI = 01
ENDIF
'm STORE NEWLY RECOVERED CASES FROM PREVIOUS IDT
’0
RSUM(2) = RSUM(2) + (INFOUT : DT)
'm CALL DELAY ROUTINE
’.
CALL DELLVFS(RINI, RT, SINFo, s, PLR, DEL, DT, KI)
'm STORE VALUES
': STORE NUMBER OF ANIMALS LEFT IN INFECTED STATE

ST'RG(2) = s
’m STORE RATE OF RECOVERY
INFOUT = RT

"” PREPARE TO INFECI' (DELAY WILL WORK TO ADD DISEASE
"” STORE NUMBER OF NEWLY INFECTED CASES FROM PREVIOUS IDT%

141

IF shff% = 0 THEN RSUM(l) = RSUM(l) + (welout ’ DT)
9.
"" STORE VALUES NECESSARY FOR CALCULATING INCIDENCE DENSITY
ID(l) = ID(l) + RT ‘ DT
ID(2) == ID(2) + ppn(l) ‘ DT
"" CALL DELAY ROUTINE: CREATES NEW SICK CASES
" FROM POPULATION THROUGH THE PLR
CALL DELLVFS(RINN, RT, SNONO. S, PLR, idel, DT, KN)
’t
"" STORE VALUES
" STORE NUMBER OF ANIMALS LEFT IN UNINFECTED STATE
STRG(1) = S
"“ STORE NEW RATE OF INFECTION
wclout a RT
"" STORE NEW POPULATION VALUES FOR EACH DISEASE STATE
H

FOR B = 1 TO 2
ppn(B) = mean
NEXT B

"" IF EPIDEMIC IS OFF, GENERATE RINN - 'UNINFECI‘ THE POPULATION
IF shff% = 1 THEN
RINN = welout
ELSE
RINN = 0!
END IF
NEXT T
"" IF REQUESTED, RANDOMIZE THE BETA TERM
9.
IF STOC% = 0 THEN BETAP = BETA
IF STOC% = 1 THEN
CALL EXPON(BETA, BETAP)
CALL TRIDIS(BETAMIN, BETA, BETAMAX, BETAP)
END IF
IF STOC% = 2 THEN BETAP = RND
’"‘ BREAK OUT OF LOOP IF BOTH BETA AND PPN (2) ARE TOO SMALL
u
IF ((1! - BETAP) " ppn(2)) = 1! THEN
PRINT #2, “Beta and Sick Population too small z”; D, BETAP, ppn(Z)
GOTO 900
END IF
"" GENERATE NEW INFECITON DELAY
't.
idel = (1! / (1! - (1! - BETAP) " ppn(2)))
"SWITCH OFF EPIDEMIC IF DISEASE REPRODUCITON INDEX FALLS OFF
’ IF SHFF% = 0 AND INFOUT > (PPN(1) / IDEL) THEN
IF Shff% = 0 AND INFOUT > wclout THEN
shff% a: 1
PRINT #2, 'Epidemic Off on day '; D, “Sick '; RSUM(l)
GOTO 800
END IF
9.
"“ IF SELECTED, PRINT DAILY RESULTS
IF PRDAY% THEN
PRINT #2, ”Day "; D; "Not Sick '; ppn(l), "Sick '; ppn(2);

142

'Total';(ppn(1) + ppn(2))
RINT #2, "Recovered out: ";RSUM(2), "Dead/Culled: ";
(PLROUT(1,1) + PLROUT(I, 2)), "I"; (PLROUT(2, 1) + PLROUT(2, 2))
END IF
NEXT D
800 ’ come here if epid. stops
’“' CALCULATE AND SUM ATTACK RATE(S)
’0
ATI'RAT -= RSUM(I) / (Oppn(l) + Oppn(2))
SUMAT'RT =- SUMATRT + ATTRAT
’"‘ CAPTURE NEW CASES IN HISTOGRAM GENERATION
FOR I = 1 TO 20
IF RSUM(l) >= BAR(l, I) THEN
IF RSUM(l) <2 BAR(Z, I) THEN
BAR(3, I) = BAR(3, I) + 1
END IF
END IF
NEXT I
"” PRINT OUT RESULTS AT END OF RUN
m
900 IF D > NDAYS% TT-IEN D = NDAYS%
’ PRINT #2, D; " Days Run, ", "Total at End"; ( PPN (1) + PPN (2) )
’ PRINT #2, "Total Sick"; RSUM (1), "Total Recovered"; RSUM (2)
’ PRINT #2, "Beta P: "; BETAP; " Attack Rate: "; ATTRAT
’ PRINT #2, "Culling: "; ( PLROUT (1,1) + plrout (1,2) ), "Dying:
'; ( PLROUT (2,1) + plrout (2,2) )
PRINT #2, "Conservation Check: "; (ppn(l) + ppn(2) + RSUM(2) +
PLROUT(l, 1) + PLROUT(I, 2) + PLROUT(2, 1) + PLROUT(2, 2))
PRINT #2, "percent error: "; (100 ‘ ((ppn(1) + ppn(2) + RSUM(2)
+ PLROUT(I, 1) + PLROUT(l, 2) + PLROUT(2, 1) + PLROUT(2, 2)) -

(Oppn(l) + Oppn(2))) / (Oppn(l) + Oppn(2)))
NEXT R

’"" PRINT OUT AVERAGE ATTACK RATE FOR RUNS
PRINT #2,
PRINT #2, "Average Attack Rate for "; NRUNS%; " Runs = "; (SUMATRT
/ NRUNS%)
PRINT #2,
"” PRINT OUT HISTOGRAM
9.
AS="### : ####-####:"
PRINT #3, " Runs Cases Number of Epidemios of
Indicated Size"
FOR I = 1 TO 20
PRINT #3, USING AS; BAR(3, I), BAR(l, I), BAR(Z, 1);
IF BAR(3, I) > 0 THEN
FOR J :- 1 TO BAR(3, I)
PRINT #3, "‘";
NEXT J
END IF
PRINT #3,
NEXT I
INPUT "Run again? ( 1 = Yes, 0 = No ): "; YN%
IF YN% GOTO 100
END

143

SUB EXPON (MEAN, XVAR) STATIC

’OOOOOOOOOOOOOCOOOOOOOOOO......OO.‘OCOOOttttlitttitttttttttttttOOQOOOI
O

" THIS SUBROUTINE COMPUTES AN EXPONENTIALLY DISTRIBUTED RANDOM
VARIABLE

" MEAN : THE EXPECTED VALUE OF THE VARIABLE

"' XVAR : THE EXPONENTIALLY DISTRIBUTED RANDOM VARIABLE

’00........0.0000000000000000000UOI.IOIOOOIIIOOOOOOOOOO......OOOIOO.
9.

”FOR A = 1 TO 3
RRR = RND
XVAR = -MEAN ‘ LOG(RRR)
”NEXT A
END SUB
STOP

’ ” SUBROUTINE DELLVFS - DISTRIBUTED DELAY WITH TIME VARIATIONS -
5/12/89

9 t.IO.itt.Oi...ttfittt*ltfilitt.fitfitttfittttttttltttfittitttttitttttttttttttt.

' m VARIABLE DICTIONARY

’ Ottttflfittttitttttfii......l.0“.0.00000000.itOtttttttttifittttttfiiltlOttfitt
’ Otttttlillltfififittttfitt.ttt FROM MAIN PROGRAM CALL:

' " RIN : INPUT TO POPULATION DURING DELAY

' " ROUT : EXIT DUE TO DELAY

' " ST (K) : STORAGES FOR K STAGES

* -- STRG : NUMBER OF UNITS LEFT IN POPULATION AFTER DELAY
' " PLR : PROPORTIONAL LOSS RATE

' " DEL : CURRENT DELAY

' " DT : DIVISION OF DAY

' n K : NUMBER OF STAGES IN DELAY

’ ....O.......OOOOOOOOOOOOOO IN’I'ERNALLY GENERATED

' " BDDl : PROPORTIONAL LOSS FACTOR

’ ...tttttttttt¢ttttttttfittfittttttttfittttttl.....OtttttttQtttttttttttOQOOQt
’ it

SUB DELLVFS (RIN, ROUT, STO, STRG, PLR, DEL, DT, K) STATIC
’ t.
’ ....tttttttttittttlttttttttttttttttttitttttttttttttttilCOIIQttttttttttt.fit
S .3 .

’ ” SET PROPORTIONAL LOSS FACTOR
BDDl = PLR + K / DEL

REM
K2 = K - 1

’0.

’ " LOOP FOR 111% SUBINTERVALS

’ O.

’ “ LOOP TO COVER THE STAGES (LAST STAGE IS HANDLED AS SPECIAL CASE
TO

’ ” COVER THE EFFECT OF ADDITIONS TO POPULATION FROM RIN)

’0.

FORI=1TOK2

’ " CALCULATE NEW STORAGES

’0.

ST(I) = ST(I) + DT . ((ST(I + 1) * (K / DEL)) - (ST(I) * BDD1))

144

NEXT I

9..

' " CALCULATE NEW STORAGES FOR SPECIAL CASE AT LAST STAGE

9..

ST(K) = ST(K) + DT ' (RIN . (ST(I) ° BDD1))
’ O.
' " FILL STORAGE WITH TOTAL NUMBER OF UNITS LEFT AT END OF DELAY
. .. (UNITS = RATE . DELAY / NUMBER OF STAGES)

STRG = 0!

FOR I = 1 TO K
STRG = STRG + ST(I)
NEXTI

’0.

’ “ SET ROUT : LOSS DUE TO DELAY

’0‘

ROUT = ST(1) / (DEL / K)

END SUB

APPENDIX D
Quick Basic code for Simulation of disease in a Dairy herd

DECLARE SUB EXPON (MEANIO, XVARIo)

DECLARE SUB ECON (OPPNo, TAGEO, P%, R, II, IDT%, NI, DTI, NDAY%, PPNI(),
PLROUTIo, VRATEIO, SUMBORNI, SUMBUYIo, NPV, MN%, NPV’VARQ)
DECLARE SUB PLRSET (AI, KI, DI, POPI, SH%, DOU’TI, DELI, D'I‘I, mort!(), CULLIo,
PLROUTIo, SELLo)

DECLARE SUB DELLVYS (AINI, DINIo, RIo, AOUT‘, DOUTIo, STRGI DELI, MDELI,
PLRI, DTI, KAI, ka)

DECLARE SUB DELLVFS (RINI, ROUT', ST!0, STRGI, PLRI, DELI, DT!, KI)

A__AAAAAA AAA AAA AAAAA AAA AAAAAA AAA AAA A AA AA A LA-

- P399351“- FINBQNBAS _5/10/99 - - ~~

DIM OPPN(3, 3), PPN(3, 5), TPOP(3), BUY(3), WEAN(5), FRESH(5)
DIM SUMINF(3), BETA(3), betaP(3), BETAMAX(3), ASUMBUY(3), SELL(3)
OPPN (A,B): ORIGINAL POPULATION - A = 1) CALVES; 2) YOUNG; 3) COWS
: DISEASE STATUS - B = 1) UNINFECTED; 2) INFECTED,
3)IMMUNE FROM DISEASE OR COLOSTRUM
PPN (A, C). POPULATION PROCESS - A = 1) CALVES; 2) YOUNG; 3) COWS
:DISEASE STATE - C = 1) RECOVERED, 2) IMMUNE;
3) INFECTED, 4) VACCINATED/COLOSTRUM; 5) WELL
TPOP (A) :TOTAL POPULATION - A = 1) CALVES; 2) YOUNG, 3) COWS
STOC% : DON’T RUN STOCHASTICALLY FLAG ( O = RANDOM, 1 = NOT)

 

’

 

U U U . U U U ' ‘ O

BETA : THE RANDOMLY GENERATED SECONDARY ATTACK RATE
BETAP : THE SECONDARY ATTACK RATE PREDICTED FROM THE

REGRESSION
’ MODEL FOR THE ANNUAL INCIDENCE DENSITY, ASSUMING

ONE
INFECTED IS PRESENT ON THE AVERAGE
BETAMAX : MAXIMUM VALUE THAT BETA CAN ASSUME
BETAMIN : MINIMUM VALUE THAT BETA CAN ASSUME
BUY (A) : PURCHASE RATE - A = 1) CALVES; 2) YOUNG; 3) COWS
WEAN (D) :WEANING RATE - D: =2) IMMUNE, 3) INFECTED,
4) VACCINATED; 5) WELL’
FRESH (C). FRESHENING RATE - C = 1) RECOVERED, 2) IMMUNE;
3) INFECTED, 4) VACCINATED, 5) WELL
DIM cum, 3), mort(3, 2), MDEL(5), DISDEL(5), Disout(3, 5)
CULL (A, C). CULLING RATE - A = 1) CALVES; 2) YOUNG; 3) COWS
- C = 1) RECOVERED, 2) IMMUNE,
3) INFECTED, 4) VACCINATED; WELL
MORT (A,B): MORTALITY RATE - A = 1) CALVES; 2 YOUNG; 3) COWS
- B =- 1) UNINFECTED; 2) INFECTED
DISDEL (C). DISEASE DELAYS - C = 1) RECOVERED, 2) IMMUNE;
3) INFECTED, 4) VACCINATED; 5) WELL
DISOUT (A, C) DISEASE MOVEMENTS - = 1) CALVES; 2) YOUNG; 3) cows
- C = 1) RECOVERED, 2) IMMUNE;
3) INFECTED, 4) VACCINATED, 5) ’WELL
DIM AGEOUT(2, 5), PLROUT(3, 4), K’K(5), VRATE(3), VOUT(3), SH%(3)
AGEOUT (A ,C) AGE GROUP MOVEMENTS A = 1) CALVES; 2) YOUNG
- C =- 1) RECOVERED, 2) IMMUNE,
3) INFECTED, 4) VACCINATED, 5) WELL
PLROUT (A,D) PLR LOSSES - A = 1) CALVES; 2) YOUNG, 3) COWS
= 1) NON-RESPIRATORY MORTALITY
= 2) NON-RESPIRATORY CULL, SALES
= 3) RESPIRATORY MORTALITY
= 4) RESPIRSATORY CULL
1

v O U 8 O U I ' O O U . ' U C . U U

Q U ' C U U U U

146

I KK (C) : STAGES FOR DISEASE - C = 1) RECOVERED, 2) IMMUNE;
I : 3) INFECTED, 4) VACCINATED, 5) WELL

I VRATE (A) :VACCINATION RATES - A = 2) YOUNG; 3) COWS’
VOUT (A) : NEWLY VACCINATEDS - A = 2) YOUNG; 3) COWS
. SH% (A) : SHUT OFF INFECTION - A = 1) CALVES; 2) YOUNG; 3) COWS
DIM ROUT(3), TROUT(3), IDmean(3), ID(3), TAGE(3), TTAGE(3), SUMOUT(3),

TSUMOUT(3), PROB(3)
I PROB(A) :PROBABILTY OF A NEW INFECTIVE BEING ADDED ANY
MONTH
ROUT (A) : NUMBERS INF’D/MON - A = 1) CALVES; 2) YOUNG; 3) COWS
TROUT (A) : NUMBERS INF’D/YR - A = 1) CALVES; 2) YOUNG; 3) COWS
IDmean(a) : THE MEAN PREDICTED ID FOR EXPON DISTRIBUTION
ID (A) : INCIDENCE DENSITIES - A = 1) CALVES; 2) YOUNG; 3) COWS
TAGE (A) : NUMBERS AGING UP/MN - A = 1) CALVES; 2) YOUNG; 3) COWS
TTAGE (A) : NUMBERS AGING UP/YR - A = 1) CALVES; 2) YOUNG; 3) COWS
SUMOUT (A): SUM OF PLR LOSSES/M - A = 1) CALVES; 2) YOUNG; 3) COWS
TSUMOUT (A): SUM OF PLR LOSSES/Y - A = 1) CALVES; 2) YOUNG; 3) COWS

DIM MI 3), MR(3), AMID(3), AMR(3), SUMBUY(3), AMON(3), tamon(3)

DIM mid 3), AMON2(3), tamon2(3), AMID2(3), Inr2(3), SAMID(3), SAMID2(3)

I MID (A) : INCIDENCE DENSITY/M - A = 1) CALVES; 2) YOUNG; 3) COWS

MR (A) : MONTHLY RISK - A = 1) CALVES; 2) YOUNG; 3) COWS
AMID (A) : ANNUAL IN. DENSITY - A = 1) CALVES; 2) YOUNG; 3) COWS
AMR (A) : ANNUAL RISK - A = 1) CALVES; 2) YOUNG; 3) COWS

SUMBUY (A): NUMBERS PURCHASED - A =- 1) CALVES; 2) YOUNG; 3) COWS
AMON (A) : SUM ANIMAL MONTHS/M - A = 1) CALVES; 2) YOUNG; 3) COWS
,.TAMQN (A)--E§HM..ANIMAL MRMH§IX7AT 1) CALVES; 2) YOUNG; 3) COWS

PREPARE FOR RUN

INPUT "Write OUTPUT to 1: Screen, 2: Printer, or 3: File - "; 1%
IF 1% = 1 THEN P3 = "SCRN:”
IF I% = 2 THEN P3 = "LPle"
IF 1% = 3 THEN INPUT "Enter File Name: "; PS
” OPEN PS FOR OUTPUT AS #2

 

. U U ‘ C U . C U

’ INPUT USER VARIABLES
112ml) 2.- 6c KK(2) = 6: KK(3) = 6: KK(4) = 6: KK(5) = 6
A =

DIM DOUTYS(KA, 5), PPNYS(KA, 5)
DIM DYS(KA), YOLDR(KA), YOLDV(KA), DIN(KA)

KMAx=o
FOR D = 2 To 5
IF KK(D) > KMAx THEN KMAx = KK(D)
NEXT D
DIM CALF(5, KMAX), COW(5, KMAX), P(KMAX)
IF KK(1)> KMAX THEN KMAX = KK(I)
.. DIM YNG(5, KA, KMAX), PY(KA, KMAX)

100 INPUT ”Do you want MONTHLY PRINT OUT also CID)"; MN%
INPUT "Would you like to run 3 FINANCES? (Y/N)"; ES
INPUT "Run with random variation? ( 1= Yes, 0 = No )I", STOC%
IF STOC% = 1 THEN
PRINT #2, "RANDOMIZE ON !!!, MONTHLY"

147

I VRATE (A) :VACCINATION RATES - A = 2) YOUNG; 3) COWS’
VOUT (A) : NEWLY VACCINATEDS - A = 2) YOUNG; 3) COWS
I SH% (A) : SHUT OFF INFECTION - A = 1) CALVES; 2) YOUNG; 3) COWS
DIM ROUT(3), TROUT(3), IDmean(3), ID(3), TAGE(3), TTAGE(3),
SUMOUT(3), TSUMOUT(3), PROB(3)
I PROB(A) :PROBABILTY OF A NEW INFECTIVE BEING ADDED ANY
MONTH
I ROUT (A) : NUMBERS INFID/MON - A = 1) CALVES; 2) YOUNG; 3) COWS
I TROUT (A) :NUMBERS INF’D/YR - A = 1) CALVES; 2) YOUNG; 3) COWS
I IDmean(a) : THE MEAN PREDICTED ID FOR EXPON DISTRIBUTION
. ID (A) : INCIDENCE DENSITIES - A = 1) CALVES; 2) YOUNG; 3) COWS
C TAGE (A) : NUMBERS AGING UP/MN - A = 1) CALVES; 2) YOUNG; 3)
OWS
I TTAGE (A) : NUMBERS AGING UP/YR - A = 1) CALVES; 2) YOUNG; 3)
COWS
’COSUMOUT (A): SUM OF PLR LOSSES/M - A =- 1) CALVES; 2) YOUNG; 3)
ws
’COTSUMOUT (A) SUM OF PLR LOSSES/Y - A = 1) CALVES; 2) YOUNG; 3)
ws
DIM MI 3), MR(3), AMID(3), AMR(3), SUMBUY(3), AMON(3), tamon(3)
DIM mid 3), AMON2(3), tamon2(3), AMID2(3), mr2(3), SAMID(3), SAMID2(3)
. MID (A) : INCIDENCE DENSITY/M - A = 1) CALVES; 2) YOUNG; 3)

COWS

I MR (A) : MONTHLY RISK - A = 1) CALVES; 2) YOUNG; 3) COWS

I AMID (A) :ANNUAL IN. DENSITY - A = 1) CALVES; 2) YOUNG; 3) COWS
I AMR (A) : ANNUAL RISK - A = 1) CALVES; 2) YOUNG; 3) COWS

I SUMBUY (A): NUMBERS PURCHASED - A = 1) CALVES; 2) YOUNG; 3)
ESAWVIEON (A) : SUM ANIMAL MONTHS/M - A = 1) CALVES; 2) YOUNG; 3)

’CO'wSMON (A) : SUM ANIMAL MONTHS/Y - A -- 1) CALVES; 2) YOUNG; 3)
. V PREPARE FOR RUN _

A AAA A AA AAAAA AAA AAA A A A- AA

INPUT ”Write OUTPUT to 1: Screen, 2: Printer, or 3: File - "; 1%
IF 1% = 1 THEN P3 = ”SCRNz"
IF 1% = 2 THEN P3 = "LPTI:"
IF 1% =- 3 THEN INPUT "Enter File Name: "; P3
OPEN PS FOR OUTPUT AS #2

INPUT USER VARIABLES
Elia) Z 6: KK(2) = 6: KK(3) = 6; KK(4) = 5- KK(5) = 6

DIM DOUTYS(KA, 5), PPNYS(KA, 5)
DIM DYS(KA), YOLDR(KA), YOLDV(KA), DIN(KA)

KMAX=0
FOR D = 2 TO 5

IF KK(D) > KMAX THEN KMAX = KK(D)
NEXT D

DIM CALF(5, KMAX), COW(5, KMAX), P(KMAX)
IF KK(1)> KMAX THEN KMAX = KK(I)

DIM YNG(5, KA, KMAX), PY(KA, KMAX)

. Q . v s
>

148

100 INPUT "Do you want MONTHLY PRINT OUT also (1/0):"; MN%
INPUT ”Would you like to run 3 FINANCES? (Y/N)"; ES
INPUT ”Run With random variation? ( 1== Yes, 0 = No )", STOC%
IF ST OC% == 1 THEN
PRINT #2, "RANDOMIZE ON !!, MONTHLY"
RANDOMIZE TIMER
END IF

INPUT "Enter number of runs you wish to perform: "; NRUNS%
INPUT "Enter number of days each run lasts: "; NDAYS%
INPUT ”Enter number of divisions per day (l/dt): "; IDT%
DT = 1! / IDT%
NID = NRUNS% ‘ (NDAYS% / 360) ’number of aID’s run if >360 days
DIM IDVAR(3, NID), SUMSQU(3), SUMVAL(3), VARIAN(3),
NPVVAR(NRUNS%)

I SET STARTING SECONDARY ATTACK RATES AS A FUNCTION OF
ANNUAL ID’S
PROB(I) - 15: PROB(2) - .07: PROB(3) = .06

INPUT "COMMENT“; CMS
”END IF
FOR P% -I 1 TO 1
IF P% =- 1 THEN
P3 =- "basereal"
IF 1% = 3 THEN OPEN PS FOR OUTPUT AS #2
PRINT #2, FINRUN '; P%
OPPN 1, 1) = 11: OPPN(I, 2) == 0: OPPN(I, 3) = 0
OPPN 2, 1) = 41: OPPNEI, 2) =- 0: OPPNél, 3) = O
OPPN3,1)=81:OPPN1,2)=-O:OPPN1,3)=0
PROB(I) = 0': PROB(2) = 0!: PROB(3) = O!
betaP(l) = .0000001: betaP(2) = .000000001#: betaP(3) = .000000001#
IDmean(l) = .00000001#: IDmean(Z) - .000000001#: IDmean(3) = .000000001#
CMS 8 "BASELINE_REAL "
END IF
IF P% 8 2 THEN
PS 8 "DlREAL"
CMS 8 "DISEASELREAL"
IF 1% = 3 THEN OPEN PS FOR OUTPUT AS #2
PRINT #2, ““““““ F INRUN ; P%
OPPNEI, 1) =- 11: OPPN(l, 2) =- 0. OPPN(I, 3) = O
OPPN 2, 1) - 41: OPPN(I, 2) = (I OPPN(I, 3) = O
OPPN(3, 1) = 81: OPPN(l, 2) = 0: OPPN(I, 3) = 0
PROB(I) = .15: PROB(2) = .07: PROB(3) = .06
betaP(l) = .106#: betaP(2) = .019: betaP(3) = .005
IDmean(I) a .03#: IDmean(Z) = .005: IDmean(3) = .002
END IF
IF P% a 3 THEN
P5 = "DZREAL"
CM$ = "DISEASE2_REAL"
IF 1% = 3 THEN OPEN PS FOR OUTPUT AS #2
PRINT #2, ”WT FINRUN ‘; P%

OPPN(I, 1) =- 11: OPPN(1, 2) = o OPPN(I, 3)
OPPN 2, 1) = 41: OPPN(l, 2) = o OPPN(I, 3)
OPPN(3, 1) = 81: OPPN(I, 2) = o OPPN(I, 3)
PROB(l) = .15: PROB(2) = .07: PROB(3) = .06

9

 

 

 

 

 

0
0
O

149

betaP(l) 8 3#: betaP(2) = .019 betaP(3) = .01
IDmean(l) =- .08#: IDmean(2) = .005: IDmean(3) = .0034

END IF
IF P% = 4 THEN
P3 =- ”d3real.TST"
IF 1% =- 3 THEN OPEN PS FOR OUTPUT AS #2
PRINT #2, FINRUN ; P%

 

 

OPPNEI, 1) 8 9: OPPN(I, 2) = 2: OPPN(I, 3) = 0
OPPN 2 1) =- 39 OPPN 1, 2) - 2: OPPNEI, 3) == 0
OPPN 3, 1) a 79: OPPN 1, 2) =- 2: OPPN 1, 3) = 0
PRO 1) =- .15: PROB(2) = .07: PROB(3) = .06
betaP(l) = .2: betaP(2) = .04: betaP(3) = .01#
IDmean(l) = .03: IDmean(Z) = .005: IDmean(3) = .002
CMS = "DISEASE3_REAL "

 

 

END IF
1F P% I 5 THEN
P3 - "D4REALTST"
IF 1% =- 3 THEN OPEN PS FOR OUTPUT AS #2
PRINT #2, ' FINRUN ; P%

OPPN(I, 1) =- 9: OPPN(I, 2) =- 2: OPPN(1, 3) == 0
OPPN 2, 1) =- 39: OPPN(1, 2) = 2: OPPNEL 3) =3 0
OPPN 3, 1) =- 79 OPPN(I, 2) = 2: OPPN 1, 3) =- 0
PRO 1) =- .15: PROB(2) =- .07: PROB(3) = .06
betaP(l) a .2: betaP(2) =- .04: betaP(3) = .01#
IDmean(l) == .03: IDmean(Z) = .005: IDmean(3) = .002
CMS = ”DISEASE4.REAL ”
END IF
’ "‘" CULL AND MORTALITY RATES - AVERAGES
WEANAGE - 120: WEANAGE2 = 140
F RESHAGE = 27: FRESHZ =- 29 ’ IN MONTHS
” VRATE(I) = .0000: FOR A = 2 TO 3: VRATE(A) = .0018: NEXT A
BUY(l) - 0!: BUY(2) - 0t BUY(3) 0!
mort(l, 1) - .001: mort(l, 2) - .02 ’=CASE FATALITY RATE
CULL(1, 1) = 0". CULL(1, 2) = .000006: SELL(l) == 0!

mort(2, 1) a .oooo24: mort(2, 2) = .013 ’=CASE FATALITY RATE
CULL(2, 1) =- 0!: CULL(2, 2) a w SELL(2) = O!

mort(3, 1) = .000106: mort(3, 2) = .000028 ’= CASE FATALITY RATE
CULL(3, 1) = .0008: CULL(3, 2) = 0

CULLBASE = CULL(3, 1)

IF P% a 5 THEN

mort(l, 2) = .07: mort(2, 2) = .07: mort(3, 2) = .07

PRINT #2, "HI CASE FATALITY 1N all ages "

END IF

BIRTH = (1! / 360) ‘" .43

FOR R = 1 TO NRUNS%

1F NRUNS% > 1 THEN
PRINT #2, : PRINT #2, "Run "; R: PRINT #2,
END IF

IMDUR = 36o INFDUR = 7: VDUR = 270
DISDE 1) = O!
DISDEL 2) = IMDUR
DISDEL(3) = INFDUR
DISDEL(4) = VDUR
DISDEL(S) = 0!

150

I DISDEL (1) AND DISDEL (5) WILL CHANGE AT EACH DT
. CONVERT WEANING AGE IN DAYS TO DAILY WEANING RATES
FOR I ... 1 To 5: WEAN(I) a 1 / WEANAGE: NEXT I
WEAN(2) = 1 / WEANAGE2
. CONVERT FRESHENING AGE AND WEANING AGE INTO DAILY RATES
FRESHR = 1/ ((FRESHAGE . 3O) - WEANAGE)
FOR I - 3 TO S:'FRESH(I) = FRESHR- NEXT I
FRESHRL - 1/(FRESH2 . 3O - WEANAGE)
FOR I - 1 To 2 FRESH(I) =- FRESHRL: NEXT I

VAGE =- 10

’ CONVERT VACCINATION AGE FROM MONTHS FROM BIRTH TO DAYS
FROM WEANING

, VAGE =- (VAGE . 30!) - (II / WEAN(5))
: ALEV ( # DAYS PER AGE LEVEL IN YOUNG STOCK )
, ALEV - ((1! / FRESH(s» - (1! I WEAN(5))) I KA

’ CREATE VLEV - AGE LEVEL WHEN YOUNG STOCK WILL BE
VACCINATED

VLEV =- INT(VAGE / ALEV)
IF VLEV < (VAGE / ALEV) THEN VLEV= VLEV + 1
VYOUT- OI

’USIENITIALIZE POPULATIONS : BOTH COUNTS AND VALUES FOR DELAY

FOR A =- 1 TO 3
SUMBUY(A) = OI
ROUT A - OI
TAGE A =- OI
SUMOUT(A) = OI

TPOP(A) = OI

NEXT A

A -- 1

PPN(A, 2) = OPPN A, 3)

PPN A, 3) =- OPPN A, 2)

APPISKA, 5) - OPPN A, 1)

PPN(A, 2) = OPPN(A, 3)
PPN A, 3) = OPPN(A, 2)
PPN(A, 5) = OPPN A, 1)

FOR K2 = 1 TO KA

 

PPNYS(K2, 2)= =OPPN 2, 3) 3K/

PPNY K2,3 =OPPN2, 2K)/

PPNY K2, =OPPN 2,1K)/
NEXT K2

REM
FOR K = 1 TO KMAX
CALF(3, K) = OPPN(1, 2) / (KK(3))
CALF(2, K)= OPPN(1, 3) / KK(2)
COW(3, K)= OPPN(3, 2) / (KK(3))
COW(2, K) = OPPN(3, 3) / KK(2)

151

CALF(5, K) = OPPN(I, 1) / (KK(5))
COW(5, K) =- OPPN(3, 1) / (KK(5))
FOR K2 = 1 TO KA
YNG 2, K2, K)= =PPNY K2, 2) / KK(2)
YNG 3, K2, K)=- -PPNY K2, 3)/ (KK(3))
YNG(5, K2, K) = PPNY K2, 5) / KK 5))
NEXT K2
NEXT K
FOR D . 1 TO 5
TPOP(A) - TPOP(A) + PPN(A, D)
NEXT D

’ AAAAAA A AAAA AAAAAAAAAAAA A A A A AAAAA

FOR N = 1 TO NDAYS%

’ RANDOMIZE STARTING NUMBER OF INFECTEDS AND SAR’S

9

FOR A = 1 TO 3
IF STOC% = 0 THEN BETA(A) = betaP(A)
ID(A) = IDmean(A)
NEXT A
IF STOC% = 1 THEN
IFN=10R(N MOD30)=0THEN
CALL EXPON(betaP0, BETAO) ’RAM
FOR A = 1 TO 3
IF RND < PROB(A) THEN
PPN(A, 3) == PPN(A, 3) + 1
ELSE PPN(A, 3) = PPN(A, 3)
END IF
NEXT A
END IF
END IF

’ COW INVENTORY CONTROL ”DAILY ”u ‘ ““““
D1FF== =-TPOP(3) (OPPN(3, 1) + OPPN(3, 2) + OPPN(3, 3))
DIFFPERB DIFF / (OPPN(3, 1) + OPPN(3, 2) + OPPN(3, 3))
IF INT(D1FF) > 0! THEN

CULL(3, 1) = DIFF "' (1 l 30) ’Increase cull to DIFF per month
BUY(3) = 0!
ELSEIF INT(D1FF) = 0! THEN
CUL 3, 1) = CULLBASE
BUY(3 = 0!
ELSE
BUY(3) =3 -DIFF ’" (1 / 30)’ buy at DIFF per month
CULL(3, 1) = CULLBASE
END IF

’ YOUNG STOCK INVENTORY CONTROL - SELL DAIRY HEIFERS IF >

ORIGINAL SIZE
DIFFYS= =II-TPOP(2) (OPPN(2, 1) + OPPN(2, 2) + OPPN(2, 3))
IF INT(D1FFYS) > 0! THEN

SELL(2)= DIFFYS‘ (1 l 30)
ELSE

SELL(2) =
END IF

 

vv— vv vvv'vv .rv vvvrv’v' vvvv vvvv'v'vv'vvv'vv‘v

FOR I = 1 TO IDT%

152
COW PROCESSING
SET VARIABLE FOR ANIMAL AGE GROUP (A)
A = 3

U C C O 0 '
4

P

’ SET DISEASE DELAYS FOR COWS
REM“ IF ALL 3 GROUPS MIX THEN INCREASE THE NUMBER OF
INFECTIVE CONTACTS

CONTACTS = "N" ”applies to all ages

IF CONTACTS = "Y" OR CONTACTS = "y" THEN

EISSIIJSMINHA) =- PPN(1, 3) + PPN(2, 3) + PPN(3, 3)

SUMINF(A) - PPN(A, 3)
END IF

IF SUMINF(A) >=- 1! THEN
IF BETA(A) < 1! THEN DISDEL(5) = (II / (LI - (LI - BETA(A)) .
SUMINF(A)»
ELSE
DISDEL(S) - 365 / ID(A)
ENDIF

9

Compute more accurate # at risk
AMON2(A) - AMON2(A) + DT" (PPN(A, 5)) / 30!

I HOLD RECOVERING (DISOUT (A2» AND UNVACCINATING
(DISOUT(A ,4)) COWS

OLDM= ==Disout(A, 2)
OLDV = Disout(A, 4)

’ LOOP FOR 4 DISEASE STATES ( NO RECOVERED STATE- ASSUME N O
LOSS)

’ FORD=2T05

’ SELECT DISEASE DELAY AND NUMBER OF STAGES, AND PUT
WORKING VS OF
’ POPULATION IN P

DEL .. DISDEL(D)
K=Kmm
FOR K2 = 1 TO K
P(K2) = COW(D, K2)
NEXT K2

’ CALCULATE RIN (ADDITIONS) INCLUDES AGING HEIFERS, AND
CHANGES IN
’ DISEASE STATES

RIN = AGEOUT(2, D)
IF D = 2 THEN RIN = RIN + Disout(A, 3)
IF D = 3 THEN RIN = RIN + Disout A, 5)
IF D = 4 THEN RIN = RIN + VOUT(A)
IF D = 5 THEN

153

RIN = RIN + OLDM + OLDV + BUY(A) + AGEOUT(2, 1)
BISIIIJDMIgUY(A) a SUMBUY(A) + (BUY(A) .. DT)

’ 1F EPIDEMIC IS OFF (SH%-1), DIVERT ’SICK’ ANIMALS BACK TO WELL
GROUP

IF SH%(A) = 1 THEN

1F D =- 3 THEN RIN = AGEOUT(2, D)

1F D =- 5 THEN RIN = RIN + Disout(A, 5)
END IF

’ CALCULATE PLR (PROPORTIONAL LOSS RATE): INCLUDES CULLS
AND MORTALITY

’ AND CALL PLRSET TO COUNT UP LOSSES BASED ON TYPE AND
DISEASE STATE

PLR =- mort(A, 1) + CULL(A, 1) + SELL(A)
IF D = 2 THEN PLR = PLR + CULL(A, 2)
IF D =- 3 THEN PLR = PLR + mort(A, 2)
IF D = 5 THEN PLR =- PLR + VRATE(A)
CALL PLRSET A, K, D, PPN(A, D), SH%(A), Disout(A, 5), DEL, DT,
mort(), CULLO, PLROUTO, S LLO)

I CALCULATE VACCINATIONS
IF D =- 5 THEN VOUT(A) == PPN(A, D) . VRATE(A)

’ CALL DELAY ROUTINE TO ADD NEWS, MOVE ANIMALS THROUGH
DISEASE STATE,
’ AND REMOVE LOSSES FROM PLR

, CALL DELLVFS(RIN, RT, P0, STRG, PLR, DEL, DT, K)

’ STORE MOVEMENT (DISOUT) AND NEW POPULATION (PPN) IF ANY
POPULATION
’ FIGURES GO < 0, ZERO ALL POPULATIONS

Disout(A, D) = RT
IF STRG > 0! THEN
PPN(A, D) = STRG
FOR K2 =- 1 TO K
COW(D, K2) = P(K2)
NEXT K2
ELSE
PPN(A, D) = 0!
FOR K2 = 1 TO K
COW(D, K2) = 0!
NEXT K2
END IF

NEXT D

TPOP(A) = OI
FOR D =1 To 5

TPOP(A) = TPOP(A) + PPN(A, D)
NEXT D

’ EPIDEMIC CHECK FOR COWS

IF PPN(A, 5) / DISDEL(5) < Disout(A, 3) THEN
” 1F DISOUT(A, 5) < DISOUT(A, 3) THEN
” IF DISOUT(A, 5) < 1 / DISDEL(3) THEN
IF SH%(A) =- 0 THEN SH%(A) = 1 ’ PRINT "Epidemic OFF for Cows,
Day "; n

ELSE
IF SH%(A) = 1 THEN SH%(A) = 0 ’ PRINT "Epidemic ON for Cows,
Day "; n

END IF

IPRINT #2, "del-"; DISDEL(5); "A”; A
”PRINT #2, "DISOUT"; DISOUT(A, 5); 'T/INFDEL"; 1 I DISDEL(3); "INFOUT";
DISOUT(A, 3)

III UPDATE ROUT

IF SH%(A) =- OI THEN ROUT(A) = ROUT(A) + Disout(A, 5) I DT
IF ROUT(A) < OI THEN ROUT(A) = OI

YOUNG STOCK PROCESSING
SET VARIABLE FOR ANIMAL AGE GROUP (A)
’ A = 2
’ SET DISEASE DELAYS FOR YOUNG STOCK

REMI- IF ALL 3 GROUPS MIX THEN INCREASE THE NUMBER OF
INFECTIVE CONTACTS
IF CONTACTS -= "Y" OR CONTACTS = "y" THEN
SUMINF(A) = PPN(I, 3) + PPN(2, 3) + PPN(3, 3)
ELSE
SUMINF(A) = PPN(A, 3)
ENDIF

IF SUMINF(A) >= II THEN
IF BETA(A) < II THEN DISDEL(5) = (1! I (1! - (1! - BETA(A)) .
SUMINF(A)» ,
ELSE
DISDEL(5) = 365 I ID(A)
ENDIF
DISDEL(I) - DISDEL(5)

O . O 0

Compute more accurate # at risk
AMON2(A) = AMON2(A) + DT "' (PPN(A, 5) + PPN(A, 1)) / 30!

’ LOOP FOR 5 DISEASE STATES
FOR D = 1 TO 5
’ SET DISEASE DELAY (DEL), MATURATION DELAY (MDEL) AND

NUMBER OF STAGES,
’ AND PUT WORING VERSION OF POPULATION IN PY

155

K =- KK(D)
DEL- =DISDEL(D)
MDEL= KA I ((1! I FRESH(D» (II I WEAN(D)))
FOR K2 =- 1 TOK

FOR K1 =- 1 To KA

PY(KI, K2) =- YNG(D, K1, K2)

NEXT K1

NEXT K2

’ CALCULATE PLR (PROPORTIONAL LOSS RATE): INCLUDES CULLS AND
MORTALITY

PLR =3 mort(A, 1) + CULL(A, 1) + SELL(A)
1F (D - 1) OR (D: 2) THEN PLR= PLR + CULL(A, 2)
IF D- 3 THEN PLR= PLR + mort(A, 2)
IF D =- 5 THEN PLR :- PLR + (VRATE(A) / KA)

’ CALCULATE AGE INPUTS (AIN) FOR YOUNG STOCK

AIN= OI
IF D > 1 THEN AIN = AGEOUT(I, D)
IF D= 5 THEN
AIN = AIN + BUY(A)
SUMBUY(A) = SUMBUY(A) + (BUY(A) I DT)
ENDIF

CALCULATE DISEASE INPUTS (DIN), AND CALL PLRSET TO COUNT UP
LOSSES BASED ON TYPE AND DISEASE STATE

CALL PLRSET(A, K, D, PPNYS(A, D), SH%(A), Disout(A, 5) DEL,
DT, mort(), CULLo, PLROUTo, SELLo)

' U . V

FOR A2 = 1 TO KA
IF D = I THEN
YOLDR(A2) = DOUTYS(A2, D)
DIN(A2) = DOUTYS(A2, 2)
ENDIF
IF D = 2 THEN DIN(A2) = DOUTYS(A2, 3)
IF D = 3 THEN DIN A2) = DOUTYS(A2, 5)
IF D = 4 THEN
YOLDV(A2) = DOUTYS(A2, D)
IF A2 = VLEV THEN DIN(A2) = VYOUT
ENDIF
, IF D = 5 THEN DIN(A2) = YOLDV(A2) + YOLDR(A2)

I IF EPIDEMIC IS OFF, DIVERT ’SICK’ ANIMALS BACK TO WELL GROUP
IF SH%(A) = 1 THEN
IF D = 3 THEN DIN(A2) = OI ’
IF D = 5 THEN DIN(A2) = DIN(A2) + DOUTYS(A2, 5) +
ENDIF
NEXT A2

IF D = 5 THEN VYOUT = PPNYS(VLEV, 5) I VRATE(A)

YOLDR(A2)

156

TAGE(A) =- TAGE(A) + (AGEOUT(A, D) I DT)
I CALL DELAY ROUTINE TO ADD NEW CASES, MOVE ANIMALS
THROUGH BOTH AGE
I AND DISEASE STATES, AND REMOVE LOSSES DUE TO PLR

DEL = K / DEL
CALL DELLVYS(AIN, DINO, PY(), AOUT, DYSO, STRG, DEL,
MDEL, PLR, DT, KA, K)

I STORE MOVEMENT (DISOUT AND AOUT) AND UPDATE NEW
POPULATIONS (PPNYS)

Disout(A, D) = 0!

FOR A2 =- 1 TO KA
DOUTYS(A2, D) = DYS(A2)
Disout(A, D) = Disout(A, D) + DYS(A2)
PPNYS(AZ, D) = 0!

NEXT A2

AGEOUT(A, D) = AOUT

IF STRG > 0! THEN
8% = 1

ELSE
S% = 0

END IF

PPN(2, D) =- STRG " 8%

FOR K2 = 1 TO K
FOR K1 = I To KA
YNG(D, K1, K2) = PY(K1, K2) I 5%
PPNYS(KI, D) = PPNYS(KI, D) + PY(KI, K2) I 5%
NEXT K1
NEXT K2

NEXT D

TPOP(A) =- OI
FOR D = 1 TO 5

TPOP(A) = TPOP(A) + PPN(A, D)
NEXT D

I EPIDEMIC CHECK FOR YOUNG STOCK
IF (PPN(A, 5) + PPN(A, 1)) I DISDEL(5) < Disout(A, 3) THEN

” IF DISOUT(A, 5) < DISOUT(A, 3) THEN
” 1F DISOUT A, 5) < 1 / DISDEL(3) THEN
IF SH%(A) = 0 THEN SH%(A) = 1 ’ PRINT "Epidemic OFF for
Young Stock, Day "; n

ELSE

9

IF SH%(A) = 1 THEN SH%(A) = 0 ’ PRINT "Epidemic ON for
Young Stock, Day "; n

ENDIF

”PRINT #2, "DISOUT"; DISOUT(A, 5); "INFOUT"; DISOUT(A, 3)

”PRINT #2, "del="; DISDEL(5); "A"; A

”PRINT #2, "DISOUT"; DISOUT(A, 5),"1/INFDEL";1 I DISDEL(3), "INFOUT';
DISOUT(A, 3)

157

III UPDATE ROUT
IF SH%(A) =- OI THEN ROUT(A) = ROUT(A) + (Disout(A, 5) +

Disout(A, 1)) " DT
IF ROUT(A) < 0! THEN ROUT(A) == 0!

AA A A AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A

CALF PROCESSING
SET VARIABLE FOR ANIMAL AGE GROUP (A)
A = 1

U . C U . ‘

I SET DISEASE DELAYS FOR CALVES
REMII IF ALL 3 GROUPS MIX THEN INCREASE THE NUMBER OF
INFECTIVE CONTACTS
IF CONTACTS = "Y" OR CONTACTS = "y" THEN
SUMINF(A) a PPN(I, 3) + PPN(2, 3) + PPN(3, 3)
ELSE
SUMINF(A) - PPN(A, 3)
ENDIF

IF SUMINF(A) >= II THEN
IF BETA(A) < II THEN DISDEL(5) = (1! I (II - (II - BETA(A)) .
SUMINF(A)»
ELSE

DISDEL(5) - 365 I ID(A)
ENDIF
”PRINT #2, ”dels”; DISDEL(5); ”A”; A; "SUMI"; SUMINF(A)

Compute more accurate # at risk
AMON2(A) = AMON2(A) + DT " (PPN(A, 5)) / 30#

I LOOP FOR 4 DISEASE STATES (No RECOVERED STATE - CALVES AGE
Too SOON)

FOR D = 2 TO 5
’ CALCULATE AGEOUT (AGING INTO YOUNG STOCK): CALCULATE
LIKE A PLR

AGEOUT(A, D) = PPN(A, D) I WEAN(D)
, TAGE(A) = TAGE(A) + (AGEOUT(A, D) I DT)

’ SELECT DISEASE DELAY AND NUMBER OF STAGES, AND PUT
WORKING VS OF
’ POPULATION IN P

DEL = DISDEL(D)
K = KK(D)
FOR K2 = 1 To K
P(K2) = CALF(D, K2) - (AGEOUT(A, D) I DT I K)
NEXT K2

’ CALCULATE PLR (PROPORTIONAL LOSS RATE): INCLUDES CULLS

158

AND MORTALITY
’ STORE OLD PLR VALUES (USED FOR IMMUNE, VACCINATED) FOR
N ON DELAYS

THEN, CALL PLRSET TO COUNT UP LOSSES BASED ON TYPE AND
DISEASE STATE

PLR = mort(A, 1) + CULL(A, 1),+ SELL(A)
IF D = 2 THEN PLR = PLR + CULL(A, 2)
IF D =- 3 THEN PLR == PLR + mort(A, 2)
IF D- 2 OR D- 4 THEN OLDPLR= PLROUT(A, D)
CALL PLRSET(A, K, D, PPN(A, D), SH%(A), Disout(A, 5), DEL, DT,
mort(), CULL(), PLROUTO, SELLO)

’ORMODIFY POPULATIONS, ETC. USING DELAYS (INFECTED OR WELL),
’ MAKING CHANGES MANUALLY (IMMUNE OR VACCINATED)

IFD=30RD=5THEN
IF D a 3 THEN
RIN = Disout(A, 5)
IF SH%(A) = 1 THEN RIN = 0!
ELSE
RIN = «(PPN(3, 5) + PPN(3, 3)) * BIRTH» + BUY(A)
SUMBORN = SUMBORN + DT‘" (TPOP(3) "' BIRTH)
SUMBUY(A)= SUMBUY(A) + (BUY(A) DT)
PLR= PLR + VRATE(A )
ENg: ISIIII9'O(A) = 1 THEN RIN == RIN + Disout(A, 5)
CALL DELLVFS(RIN, RT, P(), STRG, PLR, DEL, DT, K)
Disout(A, D)=
ELSE

9

S CAéCULATE RIN2 - NUMBER OF ANIMALS TO ADD TO NON-DELAY
TAT
. CALVES ( A STATE, NOT A RATE)

IF D= 2 THEN

EESIEIZ‘ Disout(A, 3)- AGEOUT(A, D)

EEgIIFS «PPN(3, 4) + PPN(3, 2))" BIRTH)- AGEOUT(A, D)

PPN(A, D) = PPN(A, D) + (RIN2 * DT) - (PLROUT(A, D) -
OLDPLR)

END IF
’ RESTORE DELAY ARRAY

IFD=3ORD=5THEN
PPN(A, D) = OI
FOR K2 = I TO K
CALF(D, K2)= P(K2)
PPN(A, Kz=D) PPN(A, D) + P(K2)
NEXT
ENDIFK2

I ZERO OUT IF POPULATION GOES NEGATIVE
IF PPN(A, D) <= OI THEN

159

PPN(A, D) . OI
FOR K2 - 1 TO K
CALF(D, K2) =- OI
NEXT K2
ENDIF

NEXT D

TPOP(A) - OI
FOR D = 1 To 5
TPOP(A) =- TPOP(A) + PPN(A, D)
NEXT D
I EPIDEMIC CHECK FOR CALVES

1F PPN(A, 5) / DISDEL(5) < Disout(A, 3) THEN
”1F DISOUT(A, 5) < DISOUT(A, 3) THEN
”IF DISOUT(A, 5) < 1 / DISDEL(3) THEN
IF SH%(A) = 0 THEN SH%(A) = 1 ’PRINT "Epidemic OFF for
Calves, Day ”; n

ELSE
IF SH%(A) = 1 THEN SH%(A) = 0 ’ PRINT "Epidemic ON for

Calves, Day "; n

END IF
”PRINT #1 "DISOUT”; DISOUT(A, 5); "INFOUT"; DISOUT(A, 3)
”PRINT #2, "del=="; DISDEL(5); "A"; A
”PRINT #2, "DISOUT“; DISOUT(A, 5); ”1/INFDEL"; 1 / DISDEL(3); "INFOUT";
DISOUT(A, 3)

III UPDATE ROUT
IF SH%(A) =- OI THEN ROUT(A) = ROUT(A) + Disout(A, 5) I DT
IF ROUT(A) < OI THEN ROUT(A) = OI

CALCULATE FINANCIAL STATISTICS: I 3-:
IF E3 = "Y" OR E3 = "y" THEN CALL ECON(OPPN(), TTAGEo, P%, R, I,
IDT%, N, DT, NDAYS%, PPNO, PLROUTo, VRATEo, SUMBORN, SUMBUYO,
NPV, MN%, NPVVARO)
NEXTI

I PRINT DAILIES

TSUM = OI

TSUMOT = OI

OSUM a OI

TSUMBUY = OI

FOR A = 1 TO 3
” TPOP(A) = 0!
’ PRINT #2, "Day "; N; ”, Age Group "; A
FOR D = 1 TO 5
IF D < 3 THEN OSUM = OSUM + OPPN(A, D)
’ PRINT #2, USING " #) ####.#### "; D, PPN (A,D);
” TPOP(A) = TPOP(A) + PPN(A, D)
NEXT D
’ PRINT #2, TPOP (A)
’ PRINT #2, "Losses: ";
SUMOUT(A) = 0!
FOR J = 1 TO 4
SUMOUT(A) = SUMOUT(A) + PLROUT(A, J)
.’ PTEXITTJ #2, USING " ###.#### "; PLROUT (AJ),

 

 

160

’ PRINT #2, SUMOUT (A)
’ IF A < 3 then PRINT #2, ”Aging Out"; TAGE (A);

”IF A - 1 THEN PRINT #2, " Diseased: ”; ROUT(A); " Check: "; (100! "
((TPOP(A) + SUMOUT(A) + TAGE(A)) - (OPPN(A, 1) + OPPN(A, 2))) / (OPPN(A, 1)
+ OPPN(A, Z))) 3
”IF A > 1 THEN PRINT #2, " Diseased: "; ROUT(A); " Check: "; (100! '"
((TPOP(A) + SUMOUT(A) + TAGE(A) - TAGE(A - 1)) - (OPPN(A, 1) + OPPN(A,
2))) / (OPPN(A, 1) + OPPN(A, 2)))

TSUM =I TSUM + TPOP(A)

TSUMOT - TSUMOT + SUMOUT(A)

TSUMBUY =- TSUMBUY + SUMBUY(A)

NEXT A

’ PRINT OUT MONTHLY STATISTICS

IF (N MOD 30) =- 0 OR N - NDAYS% THEN

IF MN% =- 1 THEN PRINT #2, " "
IF MN% = 1 THEN PRINT #2, ”######## MONTHLY DISEASE
REPORT ###########"; "M ="; N / 30
FOR A = 1 TO 3
IF MN% 8 1 THEN PRINT #2, "— A="; A, "Current Betas"; BETA(A)
IF MN% =- 1 THEN PRINT #2, "Losses";
FOR J a 1 TO 4
IF MN% == 1 THEN PRINT #2, USING " ###.#### "; PLROUT(A, J);
PLROUT(A, J) = 0!
NEXT 1
IF MN% = 1 THEN PRINT #2, ”Sumout"; SUMOUT(A)
IF A = 1 THEN
tagein = SUMBORN
ELSE
tagein == TAGE(A - 1)
END IF
1F MN% -= 1 THEN PRINT #2, ”TPop.”; TPOP(A); 'Tagein"; tagein; "Tageout";
TAGE(A); ”BUY"; SUMBUY(A); ”CASES”; ROUT(A)
NEXT A
END IF
1F (N MOD 30) =- 0 OR N = NDAYS% THEN
FOR A = 1 TO 3
AGE = -TAGE(A)
IF A > 1 THEN AGE = AGE + TAGE(A - 1)
AMON = TPOP(A) + 5 " (AGE + SUMBUY(A) - SUMOUT(A))
tamon(A) = tamon(A) + AMON
MID(A) = 100! ‘ ROUT(A) / AMON
MR(A) = 1! - EXP(-MID(A))
mid2(A) = 100! " ROUT(A) / AMON2(A)
tamon2(A) = tamon2(A) + AMON2(A)
AMON2(A) == 0
mr2(A) = 1! - EXP(-Inid2(A))
TROUT(A) = TROUT(A) + ROUT(A)
ROUT(A) = 0!
TTAGE A = TTAGE(A) + TAGE(A)
TSUMOUT(A) = TSUMOUT(A) + SUMOUT(A)
ASUMBUY(A) = ASUMBUY(A) + SUMBUY(A)
SUMOUT(A) = 0!
SUMBUY(A) = 0!
ASBORN = ASBORN + SUMBORN
SUMBORN = 0!
IF MN% = 1 THEN PRINT #2, ”Incidence density, mID(appx/exact): ";

161
MID(A); "I"; mid2(A)
1

F MN% - 1 THEN PRINT #2, "One month Risk (appx/exact): ";

MR(A); ”I“; mr2(A)

REM .. IF (N MOD 360) - 0 OR N =- NDAYS% THEN PRINT #2, .. Check:";(100!
I ((TPOP(A) + SUMOUT(A) + TAGE(A) - TAGE(A - 1)) - (OPPN(A, 1) + OPPN(A,

2) + OPPN(A, 3))) I (OPPN(A, 1) + OPPN(A, 2) + OPPN(A, 3)))
NEXT A

1F MN% .- 1 THEN PRINT #2, " Big Check % : "; 100! ‘ ((TSUM - OSUM +

TSUMOUT - TSUMBUY) / OSUM)
” END IF

FOR A =- 1 TO 3
TAGE(A) = OI
NEXT A
ENDIF

’ PRINT OUT ANNUAL STATISTICS
IF (N MOD 360) =- 0 OR N =- NDAYS% THEN

PRINT #2, W ANNUAL DISEASE STATISTICS m Year #"; N / 360

PRINT #2 CMS
1F STOC% = 1 THEN PRINT #2, "RANDOM ON M
FOR A '- 1 TO 3

IF A = I THEN ASUMBUY(A) =- ASBORN + ASUMBUY(A)

PRINT #2, "A3"; A

PRINT #2, "Current TPOP="; USING "####.#"; TPOP(A);

PRINT #2, " Infecteds="; USING "###.#"; PPN(A, 3);

PRINT #2, .. Susep’s="; USING I'###.#II; PPN(A, 5) + PPN(A, I);

PRINT #2, " Immune="; USING "###.#"; PPN(A, 2) + PPN(A, 4)

PRINT #2, ”Agedout="; USING "###.#II; TTAGE(A);
PRINT #2, .. B/purc"; USING I'###.#I; ASUMBUY(A);

PRINT #2, " Tot. Losses ="; USING "###.#"; TSUMOUT(A);

PRINT #2, " Tot. CASES=”; USING "###.#”; TROUT(A)
AMID(A) = 100! '" TROUT(A) I tamon(A

AMID2(A) = 100! " TROUT(A) / tamon A)

tamon2(A) 8 O!

TROUT(A) = 0!

tamon(A = 0!

TTAGE A) = 0!

TSUMOUT(A) = 0!

ASUMBUY(A) = 0!: ASBORN = 0!

PRINT #2, ”aID (apprx)="; USING "####.##”; AMID(A ,

PRINT #2, " aID (exact) ="; USING "####.##"; AMID A)

NEXT A
I TOTAL ANNUAL RATES FOR MULTIPLE RUNS
FOR A -- I TO 3
SAMID(A) = SAMID(A + AMID(A)
SAMID2(A) = SAMID A) + AMID2(A)
NEXT A
ENDIF

NEXT N

IIII STORE VALUES FOR VARIANCE FOR APPROX aID ‘
FOR A = 1 TO 3

I IDVAR(A, R) = AMID(A)
NEXT A

’ RESET ARRAYS FOR NEW RUNS

162

FOR D = 1 TO 5
FOR A =- 1 TO 3
VOUT(A) - 0!
PPN(A, D) =- 0!
Disout(A, D) - 0!
IF A < 3 THEN AGEOUT(A, D) =- 0'
IF D < 5 THEN PLROUT(A, D) = 0'
IF D - 1 THEN
ROUT A) =- 0!
SH%(A .
TAG A) - 0!
END IF
NEXT A
FOR A = 1 TO KA
IF D =- 1 THEN
YOLDV(A) - O!
YOLDR A) = 0!
END IF
PPNYS(A, D) a 0!
DOUTYS(A, D)= =I0!
FOR C - 1 TO KK(D)
YNG(D, A, C)=
NEXT C
NEXT A
FOR C I- 1 TO KK(D)
CALF(D, C) = 0!
COW(D, C) = 0!
NEXT C
, NEXT D U
IF R = NRUNS% AND NRUNS% > 1 THEN
1F STOC% 8 1 THEN PRINT #2, "MONTHLY RAN DZ. W
EXPONENTIAL DISTRIB."
FOR A =- 1 TO 3
PRINT #2, "Starting BETAO mean"; USING "###.#"; betaP(A)
PRINT #2, "Average aID’S (appx.) for "; NRUNS%; "Runs"; SAMID(A) /
NRUNS%; "A="; A; ""
PRINT #2, ”Average aID’s (exact) for ”; NRUNS%; "Runs"; SAMID2(A) /
NRUNS%; "A="; A
NEXT A
END IF
NEXT R

II CALCULATE VARIANCE FOR APPX aID ......
IF NRUNS% > 1 THEN
FOR A = 1 To 3
FOR R a 1 TO NID
SUMSQU(A)- SUMSQU(A) + IDVAR(A, R) 2
TIIEIXT‘RMA) =- SUMVAL(A) + IDVAR(A, R)
VARIAN(A) = (SUMSQU(A) - (SUMVAL(A) , 2 I NID)) I (NID - 1)
PRINT #2, "A”; A; "Variance"; USING II####.##"; VARIAN(A); NRUNS%;
"Runs"; ,IIISISO‘it'IrI; iUMSQWA); "SUMVAL"; SUMVAL(A)
I COMPUTE MEAN AND VARIANCE OF NPV
FOR R = 1 TO NRUNS%
NPVSUM! = NPVSUM + NPVVAR(R)

163

NPVSQU! = NPVSQU + NPVVAR(R) ‘ 2
NEXT R
NPVMEAN = NPVSUMI / NRUNS%
VARNPV = (NPVSQU! - (NPVSUM! ‘ 2 / NRUNS%» / (NRUNS% - 1)
PRINT #2, "Mean of NPV’S at end Of Run 5"; NPVMEAN; "Variance ";
VARNPV
END IF
FOR A =- 1 TO 3
SUMSQU(A) - 0!
SUMVAL(A) 8 0t VARIAN(A) = 0!
NPVSUM! *8 m NPVSQU! = 0!
FOR R = 1 TO NID: IDVAR(A, R) = 0!: NEXT R
NEXT A

BEEP
’ INPUT "Would you like to run again? ( Y/N ): "; YNS
’ IF YNS =- ”Y" OR YNS = ”y" THEN 100

SUB EXPON (MEANO, XVARO) STATIC

’ THIS SUBROUTINE COMPUTES AN EXPONENTIALLY DISTRIBUTED
RANDOM VARIABLE

’ MEAN :THE EXPECTED VALUE OF THE VARIABLE

’ XVAR : THE EXPONENTIALLY DISTRIBUTED RANDOM VARIABLE

FOR A =- 1 TO 3
RRR = RND
XVAR(A) = -MEAN(A) . LOG(RRR)
NEXT A

END SUB A

DECLARE SUB PRODN (NI, FFNI), PRODRTEEO, disrte!(), DISMILKIo, dismilktL
TOTMILKI, SOLDMILKI, DT!)

DECLARE SUB COST (NI, PPNK), DAYDRUGEO, DRUGCOS'F, DAYVETK),
VETCOST', WAGERTEI, LABRTXK), LABRCOST', VRATEIo, VACPRICEL
VACCOSTL DAYINTKIo, FEEDCOSTL FEEDTOTK), DISMILKK), FOORATEIo,

pricFEEDK), DT!) '

SUB COST (N, PPN(), DAYDRUGO, DRUOCOST, DAYVETO, VETCOST,
WAGERTE, LABRTXO, LABRCOST, VRATEo, VACPRICE, VACCOST,
ISDAIAYIINATKQ FEEDCOST, FEEDTOTO, DISMILKO, POORATEO, pricFEEDO, DT)

AT

LAAAAAA A A

’ "‘ THIS PROGRAM CALCULATES THE COSTS OF ANIMAL PRODUCTION
THAT ARE VARIABLE

’ "" ON THE NUMBER AND LEVEL OF DISEASED ANIMALS IN A DAIRY
HERD. COSTS

’ “‘ THAT ARE THE SAME FOR A DISEASED AND WELL ANIMAL ARE
IGNORED.

164

I . MILK PRODUCTION COSTS ARE NOT COMPUTED HERE SINCE THEY
ARE DONE AT THE

I .. END OF THE MONTH AS A FUNCTION OF TOTMILK PRODUCED.

III THE SUBROUTINE COMPUTES COSTS ON A DAILY (EVERY DT) BASIS.
THE TOTALS

III AT THE END OF A MONTH/YEAR ARE COMPUTED IN THE MAIN
PROGRAM AND RESET TO 0.

I II DISCARDED MILK THAT IS FED TO CALVES IS USED TO DECREASE
THE DAILY FEED

I .. OF CALVES IN THIS SUBROUTINE. AAAAAAAAAAAAAA

I IIIIIIIIII VARIABLE LIST VARIABLES ORIGINATING IN DISEASE
PROGRAM ......

I II PPN (A,C) :POPULATIONS - A = 1) CALVES; 2) YOUNG STOCK; 3) COWS
I II c =- 1) RECOVERED; 2) IMMUNE; 3) SICK;

I II 4) VACCINATED; 5) WELL

III VACCANTE FLOW (A) ?//

.... DISMILK (D). DISCARD MILK #IDAY D =1) DISCARDED ONLY, 2)
FED TO CALVES

’ m VARIABLE LIST - VARIABLES ORIGIN ATING IN THIS PROGRAM

’ " DRUG (A) : DAILY DRUG TREATMENT COSTS

’ BERUGCOST : TOTAL MONTHLY DRUG TREATMENT COSTS FOR 3
A S

’ "' VET (A) : DAILY COSTS FOR VETERINARY SERVICES FOR
TREATMENT OF CASES

’ “ VETCOST : TOTAL MONTHLY VET COSTS FOR ALL 3 AGES

’ "’ LABOR(A) : DAILY HOURS FOR CARE AND TREATMENT

’ "' LABRCOST : TOTAL MONTHLY COST OF LABOR FOR CARE AND
TREATMENT

’ “ VACC (A) : DAILY COSTS TO VACCIN ATE AGE GROUP (A)

’ " VACCOST : TOTAL MONTHLY VACCINATIONS COSTS
’STgCEKEDSICK (A) : RATE OF FEEDING TO SICK CALVES AND YOUNG

’ ” FEEDPOOR (A): RATE OF FEEDING TO POOR DOING CALVES AND
YOUNG STOCK

’ "" FEEDWELL (A): RATE OF FEEDING TO NON CLINICAL (WELL)
CALVES AND YOUNG

’ "“ FEEDTOT (A): MONTHLY TOTAL OF FEED FED IN #’S

’ *" FEEDCOST : TOTAL MONTHLY COST TO FEED CALVES AND
YOUNG ALL DISEASE

’13:) EEQRATE (A) : % OF RECOVERED AND IMMUNE THAT ARE POOR

’ **

DIM DRUG(3), VET(3), VACC(3), FEEDSICK(3), FEEDPOOR(3),
FEEDWELL(3), LABOR(3), NONPOOR(3)
G I; 61:};TSIALIZE VAR’S THAT ARE SUM OF INTEGRANDS, ACROSS AGE

’S”OEQLCULATE FEEDING RATES AND COSTS FOR CALVES AND YOUNG
T
’ h

A = 1
NONPOOR(A) = 1 POORATE(A)

FEEDSICK(A)= (PPN(A, 3) DAYINTK(A, 3))
FEEDPOOR(A)= (PPN(A, 2)I POORATE(A)I DAYINTK(A, 2))

16S

FEEDWELL(A) =- («PPN(A, 5) + PPN(A, 4) + NONPOOR(A) I PPN(A, 2)) I
DAYINTK(A, 1)) - DISMILK(2))

A .. 2
FEEDSICK(A) =- (PPN(A, 3) I DAYINTK(A, 3))
FEEDPOOR(A) - «PPN(A, 2) + PPN(A, 1)) I POORATE(A) I DAYINTK(A,

2
» FEEDWELL(A) = «PPN(A, 5) + PPN(A, 4) + NONPOOR(A) I (PPN(A, 2) +
PPN(A, 1))) I DAYINTK(A,1))

FOR A = 1 TO 2
FEEDTOT(A) = (FEEDTOT(A) + DT I (FEEDSICK(A) + FEEDPOOR(A)
+ FEEDWELL(A)))
ENEED TO ADD cow FEEDCOST FOR TOTAL II
N T A
FEEDCOST = FEEDTOT(1)I pricFEED(1) + FEEDTOT(2) I pricFEED(2)
IIPRINT #2, a; "FEEDTOT(2)”; FEEDTOT(2); "FEEDCOST"; FEEDCOST; ”price";

pricFEED(a)
A = 3

FEEDCOW = FEEDCOW + «PPN(A, 5) + PPN(A, 2) + PPN(A, 3) +
PPN(A, 4)) I DAYINTK(A, 1))

’ ” CALCULATE COST ASSOCIATED WITH TREATMENT

FOR A =1 TO 3
DRUG(A) =- PPN(A, 3) I DAYDRUG(A)
DRUGCOST . DRUGCOST + DT I DRUG(A)
VET(A) a PPN(A, 3) I DAYVET(A)
VETCOST =- VETCOST + DT I VET(A)
LABOR(A) = PPN(A, 3) I LABRTX(A) I WAGERTE
LABRCOST .. LABRCOST + DT I LABOR(A)

’ “ CALCULATE VACCINATION COSTS BASED ON FLOW INTO
V‘ACCINATED STATE ,

VACC(A) = PPN(A, 5) I VRATE(A) I VACPRICE
VACCOST = VACCOST + DT I VACC(A)
NEXT

END SUB

SUB ECON (OPPN TTAGEO, P%, R, I, IDT%, N, DT, NDAY%, PPN
PLROUTo, VRATE SUMBORN, SUMBUY_(_),_NPVA,AMN%, NPVVAR( ) STATIC

’ "' SUBROUTINE IS CALLED ONLY IF THE ECONOMIC ANALYSIS OPTION
IS ON FROM

’ “' "EPIMOD" (BIGD). IT CALCULATES ALL THE IMPORTANT FINANCIAL
INFO.

’ "" SOME SUBROUTINES ARE CALLED EVERY DT, AS THEY USE DAILY
STATE VALUES

’ "" EPIMOD. TOTAL RESULTS ARE COMPUTED EVERY 30, AND 360! DAYS.
’ "" THE NET PRESENT VALUE OF THE SERIES OF MONTHLY NET
INCOMES OVER VARIABLE

’ ‘" COSTS ARE COMPUTED AS WELL AS TOTAL FOR THE ENTIRE RUN.

’ I

’ m VARIABLE LIST - VARIABLES ORIGINATING IN DISEASE
PROGRAM m

. - - .....

’ LAL‘.
v

 

HA - LA‘ A --u A --A.;.

166

III PPN (A,C) : POPULATIONS - A - 1) CALVES; 2) YOUNG STOCK; 3) COWS
III C - 1) RECOVERED, 2 IMMUNE; 3) SICK;

III 4) VACCINATED, WELL

III PLROUT (A,B): TOT. POP. LOSSES - A =- 1) CALVES; 2) YOUNG STOCK; 3)

COWS

III - E - 1) MORT, 2) CULL, 3) RESP MORT, 4) RESP CULL
III VRATE (A) : PARAMETER FOR PORTION OF A THAT IS
VACCINATED EACH DAY -

III SUMBUY(A) : THE TOTAL NUMBER OF ANIMALS PURCHASED
SINCE BEGINNING

 

 

VARIABLES ORIGINATING IN ECON “““ -
III SOLDVAL (A,B) : VALUE OF ANIMALS SOLD
III CULLVAL (A,B) : CULL VALUES - A = 1) CALVES; 2) YOUNG STOCK; 3)

COWS

III - B =- 1) RESP. POOR DOERS; 2) WELL (NOT RESP)

I II VALMILK : VALUE OF MILK SOLD THIS MONTH

III PLRBIT (B) : SELECTED FROM PLROUT - B = 1) RESPIRATORY, 2) NOT
RESP

9

 

 

PRICE AND COST PARAMETERS USED IN ECON ‘ ‘
III DAYDRUG (A) : DAILY COST OF DRUG TREATMENT PER CASE
I II DAYVET (A) : DAILY COST OF VETERINARY SERVICES PER CASE
I II LABRTX (A) : DAILY HOURS OF LABOR PER CASE
III WAGERTE : HOURLY WAGE RATE FOR SKILLED HIRED HELP
III VACPRICE : PER DOSE PRICE OF GENERIC DISEASE VACCINE
III DAYINTK (A, F): DAILY INTAKE OF FEED PER POUND OF BODY
WEIGHT OR MILK

- 1) CALVES; 2) YOUNG STOCK; 3) COWS
III FA - 1) WELL; 2) POOR DOERS; 3) SICK
III PRICFEED (A). AVERAGE PRICE OF FEED PER POUND FOR EACH
AGE GROUP

. PRODUCTION AND GROWTH PARAMETERS *

I .2.) IPAOORATE (A). % OF RECOVERED AND IMMUNE THAT ARE POOR

D RS

GIBFAIIIAODRTE (B): DAILY RATES OF MILK PRODUCTION - 1) NOT WELL; 2)
I II DISRTE (D) : DISC. RATES - D = 1) DISCARDED ONLY; 2) FED TO
CALVES

’ AAAAA A A AAA AAAAAAAA A A AA AAA AAAAAA

I DIMENSION NEW ARRAYS

DIM PLRBIT(2), OLDPLRT(3, 2), CULLVAL(3, 2), PRODRTE(2), disrte(2),
POORATE(3)

DIM MILK(2), DISCARD(2), DISMILK(2), SOLDVAL(3, 2), OLDBUY(3),
PURPRICE(3)

DIM DAYDRUG(3), DAYVET(3), LABRTX(3), pricFEED(3), DAYINTK(3, 3),
FEEDTOT(B)

’ n

’ "“ IN ITIALIZE FOR BEGINNIG OF RUN
IF N = 1 THEN
’ ’” IN ITIALIZE PRICE VARIABLES
MILKPRIC = .12
DEACPRIC = 120
DISCOUNT = .1

 

 

167

PURPRICE(l) - 200: PURPRICE(Z) = 400: PURPRICE(3) = 1500
CULLVA 1, 1) = 1001' CULLVAL(L 2) = 120!
CULLVAL 2, 1 = 1501: CULLVAL(Z, 2) = 1000! ”sale for dairy (2,2)
CULLVAL 3, 1) = 0!: CULLVAL(3, 2) = 546
’ “ INITIALIZE COST VARIABLES
A = 1
DAYDRUG(A) = 5
DAYVET(A) = .05
LABRTX(A)= =33 ’HRS
BricFEED(A) = .05 ’3 PER POUND
AYINTK(A, 1)= 4. DAYINTK(A, 2) = 35: DAYINTK(A, 3) =

A = 2
DAYDRUG(A) = .47
DAYVET(A) = .03
LABRTX(A) = .034 ’HRS
pricFEED(A) = .03 ’3 PER POUND
DA3YINTK(A, 1) = 16h DAYINTK(A, 2) = 14!: DAYINTK(A, 3) =
A =
DAYDRUG(A) =
DAYVET(A) = .75
LABRTX(A) = .08 ’HRS
pricFEED(A) = .03 ‘3 PER POUND
WAGERTE = 55 ’ SIHR
DAYINTK(A, 1) =
VACPRICE = 1!
INTKMILK= .3 ’# of feed/pound Of milk
SH PP¥C88TMLK= .01’ VARIABLE COST/ # MILK, EG. ADVERTISING,
I N
’ "“ INITIALIZE OTHER FINANCIAL AND PRODUCTION PARAMETERS
POORATE(3) = 0. POORATE(Z) = .01: POORATE(l) = .1
PRODRTE 1) = 10': PRODRTE(2)= 41.7. disrte(1)= =:5 disrte(2) = 5

ENDIF
IF N = 1 THEN NPVLONG= 0!

IIIIIIIIIIII CALL IMPORTANT SUBROUTINES EACH DT IIII- ‘ ‘ “““““
CALL COST(N, PPN(), DAYDRUGO, DRUGCOST, DAYVET(), VETCOST,

WAGERTE, LABRTXO, LABRCOST, VRATEO, VACPRICE, VACCOST,

DAYINTKo’, FEEDCOST, FEEDTOT’o, DISMILKO, POORATEO, pricFEEDO, DT)
CALL PRODN(N, PPN(), PRODRTEo, disrte(), DISMILKo, dismilkt,

TOTMILK, SOLDMILK, DT)

, A-A-A -. -- AL- - -A-

 

 

IF ((N MOD 30)= =0 OR N= NDAY%) AND I = IDT% ATHEN
COMPUTE MONTHLY TOTALS “ ‘II‘:
: : CALUCULATE VALUE OF ANIMALS BEING SOLD

FOR A = 1 TO 3
PLRBIT(1)= PLROUT(A, 4)
PLRBIT(2)= PLROUT(A, 2)
FOR B = 1 TO 2
SOLDVAL(A, B) = CULLVAL(A, B) I PLRBIT(B)
NEXT B
NEXT A
BIRT£EACVAL~ DEACPRICI (SUMBORN) ISUMBORN IS 50% OF YTD
CALFVAL=(SOLDVAL(1, 1) + SOLDVAL(I, 2) + DEACVAL)
YNGVAL= (SOLDVAL(2, 1) + SOLDVAL(2, 2))

 

 

168

COWVAL= =,(SOLDVAL(3 1 + SOLDVAL(3, 2))
IF MN% - 1 THEN PRINT #2; IW MONTHLY FINANCIAL REPORT
W

Month #"; N / 30
IF MN% = 1 THEN PRINT #2, "INCOME”
IF MN% = 1 THEN PRINT #2, ”Animal sales:"; " Calves= S"; CALFVAL; " Young=
S"; YNGVAL; ”Cows-I S"; COWVAL
FOR A = 1 TO 3 .
FOR B = 1 TO 2
INCMCULL = INCMCULL + SOLDVAL(A, B)
SOLDVAL(A, B) - 0!
NEXT B
NEXT A
INCMCULL = INCMCULL + DEACVAL
IF MN% = 1 THEN PRINT #2, 'Total Cull income = S“; INCMCULL
’ "" MONTHLY GROSS MILK INCOME
VALMILK = SOLDMILK ‘ MILKPRIC
IF MN% = 1 THEN PRINT #2, " Milk: "; TOTMILK; "# produced, ”; SOLDMILK; "#
sold for S"; VALMILK
IF MN% = 1 THEN PRINT #2, " .Gross value of discarded Milk 3"; dismilkt ‘
MILKPRIC
’ ” GROSS MONTHLY INCOME
GMONINC = VALMILK + INCMCULL .

 

IF MN% = 1 THEN PRINT #2, " Gross monthly incomeIS";
GMONINC
’ "" TOTAL MONTHLY VARIABLE COSTS

FOR A = 1 TO 3 ’ Watch the buy rates and inventory control

PURCOST= PURCOST + (SUMBUY(A))‘ PURPRICE(A)
”’4/17/90 problem SUMBUY(A) - 0!
NEXT A
FEEDMILK = TOTMILK ‘ INTKMILK " pricFEED(3) + FEEDCOW
MLKCOST = FEEDMILK + TOTMILK ‘ VCOSTMLK
DISCOST = DRUGCOST + VETCOST + LABRCOST

MVCOST = MLKCOST + PURCOST + DRUGCOST + VETCOST +
LABRCOST + VACCOST + FEEDCOST
IF MN% = 1 THEN PRINT #2, "VARIABLE COSTSI"
IF MN% = 1 THEN PRINT #2, "Milk Production, includes variable and feed costs 3";
MLKCOST
IF MN% = 1 THEN PRINT #2, "Feeding Calves & Young S"; FEEDCOST
IF MN% = 1 THEN PRINT #2, "COW Purchases. S"; PURCOST
IF MN% = 1 THEN PRINT #2, ”Disease Expenses:"; DISCOST
IF MN% = 1 THEN PRINT #2, "Dru s S"; DRUGCOST; "Vet Exp S"; VETCOST;
"Labor 3"; LABRCOST; "Vacc"; VAC OST
IF MN% = 1 THEN PRINT #2, " Tot. Mon. Variable Cost 3";
MVCOST
’ “ GROSS MARGIN DAIRY OVER DISEASE COSTS “"

MNETINC= GMONINC- MVCOST
IF MN% = 1 THEN PRINT #2, ‘I ““““““ I ‘ DAIRY MARGIN Over Variable
Costs for Month #"; N / 30; ';'$" MNETINC I
IF; MN% = 1 THEN PRINT #2, ""

 

 

’ "" COMPUTE NET PRESENT VALUE OF SERIES OF MONTHLY
PAYMENTS

DISCOUNT = DISCOUNT / 12

NINT% = (N / 30) ’total months of run

nMON% = NINT%

”’IF N >= 360 THEN nMON% = (N MOD 360) : PRINT nMON%

169

”NPV = NPV + MNETINC / ((1 + DISCOUNT) ‘ nMON%) ’ for the year
NPVLONG = NPVLONG + MNETINC / ((1 + DISCOUNT) “ NINT%) ’for
whole run
’ " COMPUTE ANNUAL TOTALS
TGINC = TGINC + GMONINC
TMVCOST TMVCOST + MVCOST
TMARGIN = TGINC - TMVCOST
TMLKCOST - TMLKCOST + MLKCOST
TINCMCUL = TINCMCUL + INCMCULL
TVALMILK - TVALMILK + VALMILK
TDISCOST - TDISCOST + DISCOST
TVACCOST = TVACCOST + VACCOST
TFEEDCOS = TFEEDCOS + FEEDCOST
TDRUGCOS = TDRUGCOS + DRUGCOST: TVETCOST = TVETCOST +
VETCOST
TLABRCOS = TLABRCOS + LABRCOST
TPURCOST = TPURCOST + PURCOST
’ *" ZERO MONTHLY TOTALS
GMONINC = m MVCOST = 0k PURCOST = 0!
INCMCULL = 0t MLKCOST = 0!
VALMILK = 0!: SOLDMILK = 0!: TOTMILK = 0!: dismilkt = 0':
DISMILK(l) = 0!
DISMILK(Z) = 0': DISCOST = 0': DRUGCOST = 0: VETCOST - 0':
LABRCOST 0!
VACCOST = 0': FEEDCOST = 0!: FEEDTOT(I) = 0!: FEEDTOT(2) = 0!:
FEEDCOW = 0!
END IF
’ "' PRINT ANNUAL TOTALS
IF (N MOD 360) = 0 OR N = NDAY% THEN
IF I = IDT% THEN
’ "‘ ADJUST MILK PRODUCTION ACCORDING TO NEW HEIFERS
FRESHENING
IF (TTAGE(2) / (OPPN(3, 1) + OPPN(3, 2) + OPPN(3, 3))) > 3 THEN
ENTDOIIF‘RTEQ) = PRODRTE(2) " (1.02)

PRINT #2, ""

$811317 32%, " W ANNUAL FINANCIAL REPORT W Year
PRINT #2, " — ANNUAL DAIRY INCOME—z"

PRINT #2, " Total Animal Sales 3"; USING "#######.##"; TINCMCUL
PRINT #2, " Milk Sales 3"; USING "######.##"; TVALMILK
PRINT #2, " ANNUAL Gross Dairy incomeIS"; USING
"######.##”; TGIN C

PRINT #2, "— ANNUAL VARIABLE COSTS—z"

PRINT #2, "Milk Production, includes variable and feed costs 3"; USING
"######.##”; TMLKCOST

PRINT #2, ”Feeding Calves & Young S"; USING "######.##"; TFEEDCOS
PRINT #2, "Cow Purchases S"; USING "######.##"; TPURCOST

PRINT #2, "Disease Expenses S"; USING "######.##"; TDISCOST

PRINT #2, " Drugs 5"; USING "#####.##"; TDRUGCOS;

PRINT #2, " Vet Exp 5"; USING "######.##"; TVETCOST

PRINT #2, " Labor 3"; USING "#####.##"; TLABRCOS;

PRINT #2, " Vacc"; USING ”####.##"; TVACCOST

 

 

PRINT #2, " Tot. ANNUAL. Variable Cost: 3"; USING
"#######.##”; TMVCOST
PRINT #2, " "

 

PRINT #2, " - GROSS MARGIN DAIRY OVER DISEASE COSTS...$";

170

USING ”######.##"; TMARGIN

PRINT #2 "NET PRESENT VALUE of Dairy Income/Variable DISEASE
costs,RunTD S"; USING "######.##”; NPVLONG

PRINT #2, ""

PRINT #2, ”NEW dailyEprod”; PRODRTE(2)

’ “ ZERO END OF Y AR VARIABLES
TGINC = 0!: TMVCOST= 0!: TMARGIN = 0t TMLKCOST = 0!
TINCMCUL = 0'. TVALMILK = m TDISCOST = 0!: TVACCOST = 0!
TFEEDCOS = 0!: TDRUGCOS = 0! TVETCOST = 0!
TLABRCOS = 0!: TPURCOST = 0!

END IF
END IF
IF N = NDAY% AND I = IDT% THEN NPVVAR(R) = N PVLONG

’ A AAAA AA A AA A AAAAAAAAAAAAAAAAAAAAAAAA

END SUB ’ECON

SUB PRODN (N, PPN(), PRODRTEo, disrteO, DISMILKo, dismilkt, TOTMILK,

SOLDAMAILK A ADT) STATIC A

III THIS PROGRAM TRACKS HERD PRODUCTION. MILK AND ANIMAL

SALES IN MILK

IIAIgsrgRorIIDUhCTION, IT IS ASSUMED THAT SICK ANIMALS WILL PRODUCE
T A

I II HEALTHY ANIMALS, THAT SOME PRODUCTION IS DISCARDED WHEN

THE ANIMAL IS

I II SICK AND ASSUMED TO BE UNDER TREATMENT, AND THAT SOME

DISCARDED MILK

I I WILL BE FED BACK TO CALVES, WHICH WILL HELP OFFSET THE

LOSS IN MILK

III INCOME BY REDUCING THE QUANTITY OF MILK REPLACER

NEEDED TO FEED

I II CALVES IN ANIMAL SALES, IT IS ASSUMED, FOR COWS, THAT

NON-RESPIRATORY CULLS

TO \gAIrIiLEIlNCLUDE ROUTINE SALES, PRODUCTION CULLS, AND CULLS

’FBIEAUSES. IN ADDITION, IT IS ASSUMED THAT THE VALUE RECEIVED

III DIFFERENT AGE GROUPS AND CULL REASONS WILL AFFECT THE

SELLING PRICE

I II OF THE ANIMAL THESE VALUES DO NOT CONSIDER THE COST OF

REPLACEMENT. AAAAAAAAAAAAAAAAAA

I IIIIIIII VARIABLE LIST VARIABLES ORIGINATING IN DISEASE

PROGRAM III

III PPN (A,C) :POPULATIONS - A = 1) CALVES; 2) YOUNG STOCK; 3) COWS

I II c = 1) RECOVERED, 2) IMMUNE; 3) SICK;

I II 4) VACCINATED, 5) WELL

I IIIIIII VARIABLE LIST - VARIABLES ORIGINATING IN THIS PROGRAM

I III SOME VARIABLES WILL NOT BE USED IN THIS SUB. BUT

ORIGINATED HERE

I II MILKPRIC : PRICE OF MILK PER POUND

III PRODRTE (B): DAILY RATES OF MILK PRODUCTION - 1) NOT WELL;

171

2) WELL

I II DISRTE (D) :DISC. RATES - D = 1) DISCARDED ONLY; 2) FED TO
CALVES

I II MCOW (B) :MILKING POPULATIONS - 1) NOT WELL; 2) WELL

I II MILK (B) : POUNDS OF MILK PRODUCTION - B = 1) NOT WELL; 2)
WELL

I II DISMILK (D): DISCARD #S - D = 1) DISCARDED ONLY; 2) FED TO
CALVES

I II TOTMILK : TOTAL POUNDS OF MILK PRODUCED month

I “AASOLDMILKA : TOTAL POILNDS OF MAILKAAASAOALAD THIS month

DIM mcow(2), MILK(2)
’ “ CALCULATE NUMBER OF COWS MILKING

mcow(1) = PPN(3, 3)
mcow(2) = PPN(3, 2) + PPN(3, 4) + PPN(3, 5)

9”
9“

’ "‘ CALCULATE POUNDS OF MILK PRODUCED

’ “
FOR B - 1 TO 2
MILK(B) =- mcow(B) I PRODRTE(B) I a flow
TOTMILK a TOTMILK + DT I MILK(B)
.. NEXT B

’ " CALCULATE DISCARDS

’ ”
FOR D = 1 TO 2
DISMILK(D) = mcow(1) ‘ PRODRTE(l) "' disrte(D)
dismilkt = dismilkt + DISMILK(D) " DT
A. NEXT D

’ : CALCULATE VALUE OF PRODUCTION
SOLDMILK = TOTMILK - dismilkt

’H
’M

END SUB
STOP

III SUBROUTINE DELLVFS - DISTRIBUTED DELAY WITH TIME
VARIATIONS - Sill/8.9 '

’ ‘7'" L _ LYABIABLEPICTIQEARY. -.

’ TWHIUFUIIIU “TI FROM MAIN PROGRAM CALL:

’ “‘ RIN : INPUT TO POPULATION DURING DELAY

’ "' ROUT : EXIT DUE TO DELAY

’ "' ST (K) : STORAGES FOR K STAGES

’ "" STRG : NUMBER OF UNITS LEFT IN POPULATION AFTER DELAY
’ "" PLR : PROPORTION AL LOSS RATE

’ " DEL : CURRENT DELAY

’ "" DT : DIVISION OF DAY

’ """ K : NUMBER OF STAGES IN DELAY

 

 

172

 

I - I ‘ I INTERNALLY GENERATED
"T- BDDI {P.RQPQRTIQNAL LOSSEAQIQR.-- _ --

SUB DELLVFS (RIN, ROUT, ST(), STRG, PLR, DEL, DT, K) STATIC

A A AA AAAAAAAAAAA

' I.

’ ._.

’ "" SET PROPORTION AL LOSS FACTOR
REM BDDl = PLR + K / DEL

.- K2=K-1
I: LOOP FOR 111% SUBINTERVALS
I II LOOP TO COVER THE STAGES (LAST STAGE IS HANDLED AS SPECIAL
SngOIVCER THE EFFECT OF ADDITIONS TO POPULATION FROM RIN)
.. FOR I = 1 TO K2
:: CALCULATE NEW STORAGES
ST(I) = ST(I) + DT I ((ST(I + 1) I (K / DEL» - (ST(I) I BDD1))
.. NEXT I
I: CALCULATE NEW STORAGES FOR SPECIAL CASE AT LAST STAGE
ST(K) = ST(K) + DT I (RIN - (ST(I) I BDD1))

I II FILL STORAGE WITH TOTAL NUMBER OF UNITS LEFT AT END OF
’D'EL(AUYNITS = RATE I DELAY / NUMBER OF STAGES

STRG = 01

FOR I -= 1 TO K

STRG - STRG + ST(I)
NEXTI

’ M

’ fit

I : SET ROUT : LOSS DUE TO DELAY
ROUT = ST(1) / (DEL / K)
END SUB

SUB DELLVYS (AIN, DINo, R(), AOUT, DOUT(), STRG, DEL, MDEL,
PPR. DT, KA,-K'I).§T.AI 1C .....................................

’ "" THIS SUBROUTINE PERFORMS A SORT OF TWO-DIMENSIONAL
DISTRIBUTED DELAY

’ ‘" FOR YOUNG STOCK - FOR BOTH THE DISEASE PROCESSES AND THE
AQINGPROCESS

’ “ AIN - AGING INPUT - CALVES WEANING

’ *" DIN (KA) - DISEASE INPUTS - ANIMALS PROGRESSING THRU

DISEASE STATES
’ ” R (KA,KB) — ARRAY WITH STAGES

’ ”

 

173

’ “ AOUT - AGING OUTPUT - ANIMALS WHICH WILL MOVE TO THE
NEXT AGE

’ "‘ DOUT (KA) - DISEASE OUTPUT - ANIMALS PROGRESSING TO NEXT
DISEASE ST.

’ "‘“ STRG - TOTAL STORAGE = NUMBER OF ANIMALS IN THIS DELAY

’ "‘ DEL - DELAY FOR THE DISEASE PROCESS

’ " MDEL - DELAY FOR THE AGING (MATURATION) PROCESS
’ *"‘ PLR - PROPORTIONAL LOSS RATE

’ "‘ DT - DT .

’ "' KA - NUMBER OF STAGES IN AGING DELAY

“7 K I. NUMBER. OF STA95§INPISEA§E DELAY

9 u“:“ 1:“---

)fl

: :“' SET Ks FOR LOOPING

A2=KA-l
B2=kb~1

’ :“ LOOP FOR AGE AND DISEASE STAGES ‘
FOR A = 1 TO A2
...: FOR B = 1 TO BZ

I II FIRST, CALCULATE ADJUSTMENTS DUE TO AGING AND PLR
.. .AAA = (R(A + 1, B) I MDEL) - (R(A, B) I (MDEL + PLR))

ISII CAELCULATE ADJUSTMENTS DUE TO CHANGES THROUGH DISEASE
TAT
DDD = (R(A, B + 1) I DEL) - (R(A, B) I DEL)

I III CHANGE STATE
R(A, B) = R(A, B) + (DT I (AAA + DDD))

NEXT B
’ n
’ "u" SPECIAL CASE HANDLING OF LAST DISEASE STAGE : ADD IN DINs

 

9 H

7 *1

AAA = (R(A + 1, kb I MDEL) - (R(A, kb) I (MDEL + PLR))
DDD = DIN(A) - (R A, kb) I DEL)
R(A, kb) = R(A, kb) + (DT I (AAA + DDD»

.... NEXT A

’ m SPECIAL CASE HANDLING OF LAST AGE STAGE : ADD IN AIN

9 M

7 “

FOR B = 1 TO kb
AAA = AIN / kb - (R(KA, B) I (MDEL + PLR»
I AAA = AIN - (R(KA, B) I (MDEL + PLR»

1F B < kb THEN

EESDED = (R(KA, B + 1) I DEL) - (R(KA, B) I DEL)
DDD = DIN(KA) - (R(KA, B) I DEL)

ENDIF .

R(KA, B) = R(KA, B) + (DT I (AAA + DDD»

174

NEXT B
III-AIAASAUAMA AGEOAUTS FOR AOUT - MOVEMENT TO COWS

9 u

 

AOUT =- 02
FOR B - 1 TO kb
AOUT a AOUT + (R(1, B) I MDEL)
.. NEXT B

""‘"‘ CALTCUALATE STORAGE AND PREPARE DISEASE OUTS (DOUT)

 

STRG = 0!
FOR A - 1 TO KA
FOR B =- 1 TO kb
STRG = STRG + R(A, B)
NEXT B
DOUT(A) = R(A, 1) I DEL

NEXT A

’ 3*

END SUB

SUB PLRSET (A, K, D, POP, SH%, DOUT, DEL, DT, MORT(), CULL(),
PLROAUTo, ASELLQ) STATIC A A
' I II THIS SUBROUTINE CALCULATES PLR LOSSES FROM CULLILNG AND
MORTALITY FOR
I II BOTH RESPIRATORY AAND NON-RESIPRATORY CAUSES

vvrvv vv'v‘vv .v-v'vuvvvuuwrwvr vvvvvvvvvvvvv

’ "" A - AGE GROUPI . 1 - CALVES, 2 - YOUNG STOCK, 3 - COWS
’ "" K - NUMBER OF STAGES FOR CURRENT DISEASE STATE
’ "* D - DISEASE STATE

’ "" POP - POPULATION TO APPLY PLR TO

OFFDOUT - DISOUT (A5) - ADD WELL ANIMALS BACK IN IF EPIDEMIC

’ ” DEL - DELAY FOR DISEASE STATE

’2” IRS/ISRT (A,B) MORT RATE FOR A AGE GROUP, 1 = NON-RESPIRATORY,
= SP.

’ "' CULL (A,D) CULL RATE FOR A AGE GROUP, D DISEASE STATE

’ “ PLROUT (A,B)- PROPORTION AL LOSSES. 3 AGE GROUPS (INDEX A)

:C‘IULLAB: 1) NON-RESP MORT, 2) NON—RESP CULL, 3) RESP MORT, 4) RESP

vvvvvvvvv

AAAAAA A AA. AAAAA AAAA

’ FORI=1TOK

’ t.

I : CALCULATE LOSSES FOR NON-RESPIRATORY LOSSES
PLROUT(A.1)= PLROUT(A, 1) + DT I (MORT(A, 1) I POP)

175

PLROUT(A, 2) = PLROUT(A, 2) + DT I «SELL(A) + CULL(A, 1)) I POP)
IF D =- 5 AND A = 3 THEN PRINT #2, "PRLOUT,CULL"; PLROUT(A, 2); "A"; A

’ "" CALCULATE RESPIRATORY LOSSES FOR THE IMMUNE AND
INFECTED STATES

IF D = 2 THEN PLROUT(A, 4) = PLROUT(A, 4) + DT I (CULL(A, 2) I POP)
POP) IF D =- 3 THEN PLROUT A, 3) = PLROUT(A, 3) + DT I (MORT(A, 2) I

’ "' CALCULATE IN RECYCLES IF DISEASE STATE IS WELL AND
EEIDEMIC IS OFF

1F D =- 5 THEN
PLROUT(A, 1) = PLROUT(A, 1) + DT I (MORT(A, 1) I SH% I (DOUT))
PLROUT A, 2) = PLROUT(A, 2) + DT I (CULL(A, 1) I SH% I DOUT)
ENDIF
I NEXTI

v‘vvv vi vv ‘vv 7‘ wfiwvvvvv'vvwv

END SUB

BIBLIOGRAPHY

 

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