Abstract
In this paper, we consider a stochastic SEIR epidemic model with standard incidence. By constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution to the model. Our result does not depend on the positive endemic equilibrium E∗ of the deterministic system, which improves the previous result to a greater extent. Moreover, we also establish sufficient conditions for extinction of the disease.
•A stochastic SEIR epidemic model with standard incidence is studied.•We establish sufficient conditions for the existence of ergodic stationary distribution.•Our result does not depend on the positive endemic equilibrium E∗.•We establish sufficient conditions for extinction of the disease.