EPIDEMIC MODELS UNDER MOBILITY ON MULTI-LAYER NETWORKS

We study epidemic spreading models namely, SIS and SIR models, under mobility on multilayer networks. In particular, we consider a patchy environment in which each patch comprises individuals belonging the different classes, e.g., individuals in different socio-economic strata. We model the mobility of individuals of each class across different patches through an associated Continuous Time Markov Chain (CTMC). The topology of these multiple CTMCs constitute the multi-layer network of mobility. At each time, individuals in the multi-layer network of spatially-distributed patches move according to their CTMC and subsequently interact with the local individuals in the patch according to SIS or SIR models. We establish the existence of various equilibria under different parameter regimes and establish their (almost) global asymptotic stability using Lyapunov techniques. We also derive simple conditions that highlight the influence of the multi layer network on the stability of these equilibria. We numerically illustrate that the derived model provides a good approximation to the stochastic model with a finite population and also demonstrate the influence of the multi-layer network structure.Next, we extend some of the results to the case of weakly connected networks. Here, we use the notion of strongly connected components and input to state stability to study the stability of equilibria. Finally, we consider a resource allocation problem to maximize the rate of convergence to an equilibrium. We show that under certain assumptions the problem can be formulated as a geometric program. We provide numerical illustrations to corroborate the results.