The threshold of a non-autonomous SIRS epidemic model with stochastic perturbations

摘要

In this paper, we investigate a stochastic non-autonomous SIRS (susceptible-infected-recovered-susceptible) model. The extinction and the prevalence of the disease are discussed, and so, the threshold is given. Especially, we show there is a positive nontrivial periodic solution. At last, some examples and simulations are provided to illustrate our results. Copyright (C) 2016 John Wiley & Sons, Ltd.