Epidemic threshold and ergodicity of an SIS model in switched networks

Abstract

Because of individuals' random walk, such as shopping, travel, work, etc., people have different behaviors and thus have different social contact patterns. Therefore, topology of human social contact networks is time-varying. In this paper, we investigate dynamic characteristics of an SIS network epidemic model with Markovian switching. An epidemic threshold is established for the extinction and permanence of the model, which is related to the steady-state distribution of the Markov chain. An interesting result is that when the epidemic is permanent in one network but extinct in another, under network switching mechanisms, it may be either permanent or extinct depending on the steady-state distribution of the Markov chain. This reveals the important role of the Markov chain in epidemic evolution. This work shows that the epidemic propagation in switched networks is quite different from that of static networks. In addition, based on Lyapunov function method, positive recurrence and ergodicity of stochastic spreading processes are also discussed. Finally, numerical simulations are carried out to illustrate our theoretical results.