带有标准发生率和信息干预的随机时滞SIRS传染病模型的动力学行为  

Dynamic Behaviors of Stochastically Delayed SIRS Epidemic Models With Standard Incidence Rates Under Information Intervention

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

机构地区：[1]宁夏大学数学统计学院

出　　处：《应用数学和力学》2019年第12期1373-1388,共16页Applied Mathematics and Mechanics

基　　金：国家自然科学基金(11361044);宁夏自然科学基金(2019AAC03038);宁夏高等学校科学研究项目(NGY2018049)~~

摘　　要：考虑了一类具有标准发生率和信息干预的随机时滞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,从而证明了该模型正解的全局存在性和唯一性.通过构造适当的Lyapunov函数,研究了该模型的解在确定性模型无病平衡点和地方病平衡点附近的渐近行为,得到了在一定条件下随机系统的解分别围绕两个平衡点做随机振动.A class of stochastic-time-delay SIRS infectious disease models with standard incidence under information intervention were considered.A stopping time was defined.Then the existence of a unique global positive solution was proved through construction of a suitable Lyapunov function to prove the stopping time is infinite.The asymptotic behaviors of the model solution around the disease-free equilibrium point and the endemic equilibrium point of the deterministic model were studied with suitable Lyapunov functions respectively.The results show that,the solution of the stochastic system involves random vibration around the 2 equilibrium points under certain conditions respectively.

关 键 词：SIRS传染病模型 信息干预 时滞 渐近行为 

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