具有自然年龄和染病年龄的SIQS传染病模型的稳定性  

The stability of SIQS epidemic model with natural age and infection-age

作　　者：王时雯 由守科[1] WANG Shiwen;YOU Shouke(College of Mathematics and System Science,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830017

出　　处：《重庆理工大学学报（自然科学）》2022年第11期274-281,共8页Journal of Chongqing University of Technology：Natural Science

基　　金：新疆维吾尔自治区自然科学基金项目(2019D01C080,2021D01C003);新疆大学博士科研启动基金项目(62008034)。

摘　　要：建立了一类具有自然年龄和染病年龄的SIQS传染病模型。利用双曲型偏微分方程组和Volterra积分方程的相关理论方法,给出了模型的阈值R并进行稳定性分析。在总人口分布稳定的前提下,证明了当R<1时无病平衡解局部渐近稳定和全局渐近稳定;当R>1时无病平衡解不稳定且存在地方病平衡解。In this paper,a SIQS infectious disease model with natural age and infection-age is developed.By using the theory and methods of hyperbolic partial differential equations and Volterra integral equations,we obtain the threshold value of the model,and then perform the stability analysis.Under the condition of a stable population distribution,it is proved that the disease-free equilibrium solution is locally and globally asymptotically stable when R<1,and the disease-free equilibrium solution is unstable and the endemic equilibrium solution exists if R>1.

关 键 词：隔离 染病年龄 平衡解 渐近稳定 存在性 

分 类 号：O175.27[理学—数学]