一类带有接种和年龄结构的SVIR传染病模型  

An Age-Structured SVIR Epidemic Model with Vaccination

作　　者：方彬[1,2] 蔡礼明[1] 马凌霄[3] 

机构地区：[1]信阳师范学院数学与信息科学学院,河南信阳464000 [2]北京信息控制研究所,北京100037 [3]北京师范大学信息科学与技术学院,北京100875

出　　处：《生物数学学报》2014年第2期347-353,共7页Journal of Biomathematics

基　　金：国家自然科学基金(11371305)

摘　　要：数学地分析了一类带有接种和年龄结构的SVIR传染病模型的动力学性质,得到了接种疫苗策略φ和年龄a有关的基本再生数R(φ,a)的表达式,证明了当R(0,a)<1时,系统中无病平衡态是全局渐近稳定的;当R(φ,a)>1时,无病平衡态是不稳定的,此时系统至少存在一地方病平衡态.The dynamical behavior of an age-structured SVTR epidemic model with vaccination is mathematically analyzed.It is obtained for an explicit formula for the basic reproductive number R(φ) with respect to the vaccination policy φ and age a,and it is proved that the diseasefree steady state is globally asymptotically stable if R(0,a) is less than one;and is unstable if R(φ,a) is large than one.Moreover,it is showed that the age-structured model has at least an endemic steady state for R(φ,a) > 1.

关 键 词：年龄结构 基本再生数 平衡态 稳定性 

分 类 号：O175[理学—数学]