随机多群体SIRI传染病模型的动力学行为  

Dynamical Behavior of Multigroup SIRI Epidemic Model with Stochastic Perturbation

作　　者：张志成 杨志春 ZHANG Zhicheng;YANG Zhichun(College of Mathematics Science,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《应用数学学报》2023年第2期211-229,共19页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No.11971081);重庆市教育委员会科技研究重大项目(No.KJZD-M202000502);重庆市教育委员会雏鹰计划研究项目(No.CY220503)资助。

摘　　要：本文研究具有随机多群体SIRI传染病模型的动力学行为.首先建立一类具有随机白噪声的多群体SIRI传染病模型,并给出模型正解的全局存在唯一性;然后,借助基本再生数和不可约矩阵性质,通过构造一系列新的Lyapunov函数,我们获得随机模型的解分别在时间均值意义下围绕无病平衡点和地方病平衡点做随机振动的渐近行为,并给出随机振动的幅度估计;进一步地,我们得到了系统的平稳分布和遍历性,所得结果推广和改进已有工作.In this paper,we investigate the dynamical behavior of a multigroup SIRI epidemic model with stochastic perturbation.We firstly formulate a class of multi-group SIRI epidemic model with stochastic white noises and give the global existence and uniqueness of the solution of the stochastic model.Then,according to the obtained basic reproduction number and the properties of irreducible matrix,we obtain the oscillating properties of the solution of stochastic model around the disease-free equilibrium or endemic equilibrium of the deterministic model and the estimate for the oscillation amplitude is given by using some novel Lyapunov functions.Furthermore,the existence of a stationary distribution and the ergodicity of solutions are obtained.Our results extend and improve some existing ones in previous publications.

关 键 词：多群体SIRI传染病模型 随机白噪声 基本再生数 随机振动 遍历性 

分 类 号：O175.1[理学—数学]