具有非线性发生率及两个独立扰动的SIS传染病模型的动力学分析  

Dynamics of an SIS Epidemic Model with Saturation Incidence and Two Independent Perturbation

作　　者：谭杨[1] 杨林 郭子君[2] TAN Yang;YANG Lin;GUO Zijun(Tongren Polytechnic College,Tongren 554300,China;Institute of Applied Mathematics,South China Agricultural University,Guangzhou 510642,China)

机构地区：[1]铜仁职业技术学院,贵州铜仁554300 [2]华南农业大学应用数学研究所,广东广州510642

出　　处：《北华大学学报（自然科学版）》2023年第5期561-570,共10页Journal of Beihua University（Natural Science）

基　　金：铜仁市科技计划项目(2020(116号))。

摘　　要：研究具有两类随机扰动且具有非线性发生率的SIS传染病模型,通过构造Lyapunov函数方法证明了在一定条件下模型正解的存在唯一性,得到关于感染种群趋于灭绝和保持持久的充分条件,证明了平稳分布的存在并给出了数值模拟结果.Two stochastic perturbations into the SIS epidemic model with general nonlinear incidence were introduced.The existence and uniqueness of the positive solution under some condition were proved by constructing the Lyapunov function method,then the sufficient conditions for extinction and persistence were established,showed that there is a unique stationary distribution.Computer simulations were given to illustrate the results.

关 键 词：SIS传染病模型 随机微分方程 灭绝 持久 稳定分布 

分 类 号：O211.63[理学—概率论与数理统计]