随机流行病学模型的动力学行为：具有随机扰动的 SIRS 模型的平稳分布与疾病灭绝
Dynamical Behavior of a Stochastic Epidemiological Model: Stationary Distribution and Extinction of a SIRS Model with Stochastic Perturbations
AI总结：
本文研究了具有随机扰动的 SIRS 流行病学模型，利用基本再生数 $\mathscr{R}_0$ 证明了平稳分布的存在性，并揭示了随机效应导致疾病灭绝的场景，理论与数值模拟相互验证。
摘要：
本文研究了一种具有随机扰动的 SIRS 新流行病学模型。主要目标是建立唯一非负非局部解的存在性。利用从相关确定性模型导出的基本再生数 $\mathscr{R}_0$，我们证明了随机模型中平稳分布的存在性。此外，我们研究了在特定条件下确定性问题的唯一解在无病平衡点附近的波动。特别地，我们揭示了随机效应导致疾病灭绝的场景，这与确定性模型预测的持续性相反。理论分析通过数值模拟得到了补充，为我们的发现提供了进一步的验证。
英文摘要：
This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solution. Using the basic reproduction number $\mathscr{R}_0$ derived from the associated deterministic model, we demonstrate the existence of a stationary distribution in the stochastic model. In addition, we study the fluctuation of the unique solution of the deterministic problem around the disease-free equilibrium under certain conditions. In particular, we reveal scenarios where random effects induce disease extinction, contrary to the persistence predicted by the deterministic model. The theoretical insights are complemented by numerical simulations, which provide further validation of our findings.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
