Extinction and Ergodic Property of Stochastic SIS Epidemic Model with Nonlinear Incidence Rate

Abstract

We investigate a stochastic SIS model with nonlinear incidence rate. We show that there exists a unique nonnegative solution to the system, and condition for the infectious individuals $I(t)$ to be extinct is given. Moreover, we prove that the system has ergodic property. Finally, computer simulations are carried out to verify our results.