一类具有饱和发生率的随机SVIR传染病模型的平稳分布与灭绝性  

Stationary Distribution and Extinction of a Stochastic SVIR Epidemic Model with Saturation Incidence

作　　者：王津 罗超良[1] 侯爱玉[1] WANG Jin;LUO Chaoliang;HOU Aiyu(College of Science,Hunan University of Technology,Zhuzhou Hunan 412007,China)

机构地区：[1]湖南工业大学理学院,湖南株洲412007

出　　处：《湖南工业大学学报》2025年第4期82-88,共7页Journal of Hunan University of Technology

基　　金：国家自然科学基金资助项目(11801162);湖南省教育厅科学研究基金资助重点项目(21A0361)。

摘　　要：研究了一类具饱和发生率的随机SVIR传染病模型的平稳分布与灭绝性。首先,对任意的正初始值,证明该系统存在唯一的全局正解;其次,通过构造Lyapunov函数,得到当R_(0)^(s)>1时系统存在唯一遍历的平稳分布;最后,证明当R_(0)^(s)时>1时疾病将以指数灭绝。The focus of the current investigation is on the stationary distribution and extinction of a class of stochastic SVIR epidemic model with saturation incidence.Firstly,for any positive initial value,it is proven there is a unique global positive solution for the system;secondly,by constructing a Lyapunov function,there always exists a stationary distribution with a unique traversal with R_(0)^(s)>1.Finally,it is proven that the disease will become exponentially extinct with R_(0)^(s)>1.

关 键 词：随机SVIR模型 饱和发生率 治疗函数 平稳分布 灭绝性 

分 类 号：O175[理学—数学]