Dynamical behavior of a stochastic SEI epidemic model with saturation incidence and logistic growth

In this paper, we investigate the dynamical behavior of a stochastic SEI epidemic model with saturation incidence and logistic growth. Firstly, by constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the solutions to the model. Then we obtain sufficient conditions for extinction of the disease in two cases, that is, the first case is that the susceptible population survival and infected and exposed populations extinction: the second case is that all the populations extinction. (C) 2019 Published by Elsevier B.V.