Persistence and Extinction of a Stochastic SIS Epidemic Model with Double Epidemic Hypothesis

Abstract

In this paper, we aim at dynamical behaviors of a stochastic SIS epidemic model with double epidemic hypothesis. Sufficient conditions for the extinction and persistence in mean are derived via constructing suitable functions. We obtain a threshold of stochastic SIS epidemic model, which determines how the diseases spread when the white noises are small. Numerical simulations are used to illustrate the efficiency of the main results of this article.