Stationary distribution of a stochastic delayed SVEIR epidemic model with vaccination and saturation incidence

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.