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 $R_0^s>1$. Then the sufficient condition $R_0^e<1$ for the exponential extinction is also established. Results show that the values go to the deterministic basic reproduction number $R_0$ as the intensity of volatility tends to 0.

中文翻译：

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包含 Ornstein-Uhlenbeck 过程的随机 SVEIS 流行病模型的平稳分布和消亡

在本文中，我们假设 SVEIS 流行病模型中的参数满足均值回归 Ornstein-Uhlenbeck 过程，并提出了一种新的随机 SVEIS 模型。通过构造合适的 Lyapunov 函数，我们证明了该随机模型在临界值$R_0^s>1$. 那么充分条件$R_0^e<1$因为指数消光也成立。结果表明，这些值达到了确定的基本再生数$R_0$因为波动强度趋于0。