一类具有无症状感染及接种疫苗的随机SAIRS传染病模型的平稳分布

The Stationary Distribution of a Stochastic SAIRS Infectious Disease Model with Asymptomatic Infections and Vaccination

摘要: 本文综合研究了一类无症状感染，有症状感染，以及接种疫苗的随机SAIRS传染病模型的平稳分布，首先证明了模型正解的存在唯一性。然后，利用构造Lyapunov函数的方法建立了参数${ℛ}_0^s$ ，并且证明了当${ℛ}_0^s>1$ 时，模型的解在${ℝ}_{+}^3$ 上存在一个唯一的平稳分布。最后，对本文主要研究内容进行了总结，发现${ℛ}_0^s$ 受到白噪声的影响，并且${ℛ}_0^s$ 小于等于确定型SAIRS模型的基本再生数${ℛ}_0$ 。

Abstract: This article comprehensively studies the stationary distribution of a stochastic SAIRS infectious disease model with asymptomatic infection, symptomatic infection, and vaccination. Firstly, we prove the existence and uniqueness of the positive solution of the model. Then, we established the parameters ${ℛ}_0^s$ by using the method of constructing Lyapunov function, and proven that when ${ℛ}_0^s>1$ , the solution of the model has a unique stationary distribution in ${ℝ}_{+}^3$ . Finally, we summarize the main results of this article and find that ${ℛ}_0^s$ is affected by white noise. In addition, ${ℛ}_0^s$ is less than or equal to the basic reproduction number ${ℛ}_0$ of the deterministic SAIRS model.