一类受媒体报道影响的随机SIS流行病模型的研究
Stochastic SIS Epidemic Model with Media Coverage
摘要: 本文研究了一类受媒体报道影响且恢复率受到环境噪声影响的随机SIS流行病模型。利用停时理论和Lyapunov分析法，首先证明了随机模型正解的全局存在唯一性。其次，证明了随机模型的无病平衡点的随机稳定性。当确定性模型基本再生数大于１时，得到了随机模型的解在相应确定性模型的地方性平衡点附近的振荡行为，并得到了强噪声可以导致疾病灭绝的结论。通过数值模拟验证了本文的理论结果。
Abstract: A stochastic SIS epidemic model with media coverage is concerned. By stopping time theory and Lyapunov analysis, we first obtain the global existence and uniqueness of the positive solution. Then, we prove the stochastic asymptotical stability of the disease-free equilibrium point. When the basic reproduction number of the deterministic model is greater than 1, the solution of the stochastic model is oscillating around the local equilibrium point of the corresponding deterministic model, and the conclusion that strong noise can lead to disease extinction is obtained. Numerical simula-tions verify the theoretical results.
文章引用：曾琪, 周艳丽. 一类受媒体报道影响的随机SIS流行病模型的研究[J]. 应用数学进展, 2022, 11(9): 6307-6316. https://doi.org/10.12677/AAM.2022.119666

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