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.
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)
关键词
年龄结构
基本再生数
平衡态
稳定性
Age-structure
Basic reproductive number
Equilibrium
Stability
