Random migration processes between two stochastic epidemic centers

•A simple network of two stochastic epidemic centers coupled by random migration is modeled.•The interaction between susceptible/infected/removed individuals as well as their migration is described by a Markov chain.•The mean field dynamics shows that the host (resident) and guest (visitor) individuals should be accounted separately.•It is shown that the small initial contagion (SIC) approximation (being much faster in terms of the CPU time than the direct numerical simulation) gives good estimates for the mean value and the standard deviation of number of infective individuals. We consider the epidemic dynamics in stochastic interacting population centers coupled by random migration. Both the epidemic and the migration processes are modeled by Markov chains. We derive explicit formulae for the probability distribution of the migration process, and explore the dependence of outbreak patterns on initial parameters, population sizes and coupling parameters, using analytical and numerical methods. We show the importance of considering the movement of resident and visitor individuals separately. The mean field approximation for a general migration process is derived and an approximate method that allows the computation of statistical moments for networks with highly populated centers is proposed and tested numerically.