Kolmogorov equations applied to an SIS-coupled epidemiological model

Mathematical modeling of infectious diseases is necessary to study patterns of transmission and propagation that can potentially help public health officials to make better decisions to mitigate epidemic outbreaks. Both discrete and continuous population models can give insight into the approximations of the modeling approaches we implement. Metapopulation models in which we examine disease dynamics on separate patches and allow movement of the population between the patches have become increasingly popular to model the spread of diseases over geographically distinct regions. We use the forward Kolmogorov equations and present a formal proof that states that the deterministic model is in fact the expected value of the continuous-time Markov chain stochastic model trials. We show the connection between both modeling approaches in an SIS metapopulation model. We present the results of simulations to illustrate the results for different values of R₀, the basic reproductive number.