带有标准发生率和信息干预的随机SIRS传染病模型的灭绝性和平稳分布  

Extinction and Stationary Distribution of a Stochastic SIRS Epidemic Model with Standard Incidence and Information

作　　者：赵英英 胡华 ZHAO Yingying;HU Hua(School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, China)

机构地区：[1]宁夏大学数学统计学院,宁夏银川750021

出　　处：《应用数学》2018年第3期704-713,共10页Mathematica Applicata

基　　金：国家自然科学基金项目(11361044);宁夏自治区研究生教育创新计划项目(YKC201709);宁夏大学研究生创新项目(GIP2017047)

摘　　要：本文考虑了一类具有标准发生率和信息干预的随机SIRS传染病模型.定义了一个停时,通过构造适当的Lyapunov函数证明了停时为无穷大,从而证明了该模型唯一正解的全局存在性.通过构造紧集和适当的Lyapunov函数,证明模型解的平稳分布的存在性及其遍历性.此外还证明了疾病的灭绝性.In this paper, we consider a novel stochastic SIRS epidemic model with standard incidence incorporating information intervention. We first define a stopping time. Then the existence of a unique global positive solution is proved by constructing a suitable Lyapunov function to prove the stopping time is infinite. The stationary distribution and ergodicity of the model are showed by constructing a compact set and appropriate Lyapunov function. It is also proved that the extinction of the disease.

关 键 词：SIRS传染病模型 信息干预 灭绝性 平稳分布 遍历性 

分 类 号：O211.63[理学—概率论与数理统计] O175.13[理学—数学]