Abstract
In this paper, we develop and analyze a stochastic delayed SVEIR epidemic model with vaccination and saturation incidence. By constructing a suitable stochastic Lyapunov function, we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. The existence of a stationary distribution implies stochastic weak stability. Numerical simulations are introduced to illustrate the analytical result.
•A stochastic delayed SVEIR epidemic model with vaccination is studied.•We establish sufficient conditions for the existence of a unique ergodic stationary distribution.•The existence of a stationary distribution implies stochastic weak stability.