Stationary distribution and extinction of a stochastic SVEIS epidemic model incorporating Ornstein–Uhlenbeck process

In this paper, we assumed that the parameter in the SVEIS epidemic model satisfies the mean-reverting Ornstein–Uhlenbeck process, and propose a new stochastic SVEIS model. Through constructing suitable Lyapunov function, we prove that this stochastic model has a stationary distribution when the critical value R0s>1. Then the sufficient condition R0e<1 for the exponential extinction is also established. Results show that the values go to the deterministic basic reproduction number R0 as the intensity of volatility tends to 0.