一类具有年龄结构和时滞效应的复发性传染病模型的动力学分析  

Dynamic Analysis of a Type of Recurrent Infectious Disease Model with Age Structure and Time Delay Effect

作　　者：吴笛[1] 乔彦赫 徐国明[2] 曹慧[1] WU Di;QIAO Yanhe;XU Guoming;CAO Hui(College of Mathematics and Data Science,Shaanxi University of Science&Technology,Xi′an,Shaanxi 710021,China;College of Mathematical Sciences,Baotou Teachers′College,Baotou,Inner Mongolia 014030,China)

机构地区：[1]陕西科技大学数学与数据科学学院,陕西西安710021 [2]包头师范学院数学科学学院,内蒙古包头014030

出　　处：《数学建模及其应用》2023年第4期7-14,共8页Mathematical Modeling and Its Applications

基　　金：国家自然科学基金面上项目(11971281);内蒙古自治区高等学校科学技术研究项目(NJZY22036)。

摘　　要：构建并研究了一类具有免疫年龄结构和时滞效应的复发性传染病动力学模型,给出了无病平衡点全局稳定条件、地方病平衡点存在和局部稳定条件以及模型发生Hopf分支的条件.理论研究表明,随着获得性免疫失效所需时间的增加,复发性传染病会经历周期性行为,或者非周期性行为.This paper constructs and studies a class of dynamic models of recurrent infectious diseases with immune age structure and time delay effect.We give the condition of global stability of disease-free equilibrium point,the condition of local equilibrium point existence and local stability,and the condition of Hopf bifurcation of model occurrence.Theoretical studies suggest that recurrent infectious diseases experience non-cyclical or cyclical behaviors as the time required for acquired immune failure increases.

关 键 词：复发性传染病 年龄结构 时滞效应 稳定性 HOPF分支 

分 类 号：O175[理学—数学]