受环境扰动的随机SIRS传染病模型的动力学分析  

Dynamic analysis of a stochastic SIRS epidemic model subjected to environmental disturbance

作　　者：何雪晴 韦煜明 HE Xueqing;WEI Yuming(College of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541000,China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541000

出　　处：《阜阳师范大学学报（自然科学版）》2021年第2期11-16,共6页Journal of Fuyang Normal University:Natural Science

基　　金：国家自然科学基金项目(11961074);广西科技基地和人才专项(2018AD19211)资助。

摘　　要：建立一类受环境扰动的随机SIRS传染病模型来分析其动力学行为。首先证明了该模型对任意的正初始值具有唯一的全局正解,其次根据所构造的李雅普诺夫函数,应用伊藤公式讨论了疾病灭绝的充分条件,以及疾病在均值意义下的持久性,最后数值模拟验证了理论结果。The dynamic behavior is analyzed by developing a class of stochastic SIRS epidemic model subjected to environmental disturbance.The model is first shown to have a unique global positive solution for any positive initial value.Secondly,the surfficient conditions for disease extinction and its persistence in the mean sense are discussed according to the constructed Lyapunov function and using the Ito formula.Finally,the theoretical results are verified by numerical simulations.

关 键 词：基本再生数 LIAPUNOV函数 公式 灭绝性 持久性 

分 类 号：O193[理学—数学]