A STOCHASTIC THRESHOLD FOR AN EPIDEMIC MODEL WITH ISOLATION AND A NON LINEAR INCIDENCE

Abstract

In this paper, we study a stochastic epidemic model with isolation and nonlinear incidence. In particular, we propose a stochastic threshold for the model without any sharp su cient assumptions on model parameters as compared to existing works. Firstly, we establish the uniqueness of the global positive solution according to Lyapunov function method. Secondly, we prove stochastic permanence of the solutions. Then, we establish su cient condition for the extinction. Thirdly, we investigate necessary and su cient conditions for persistence in mean of the disease. Finally, we provide some numerical simulations to illustrate our theoretical results.