摘要
研究了一类具有垂直传染的年龄结构SIS传染病模型。在总人口规模不变的假设下,得到了疾病消亡与否的基本再生数T的表达式。证明了当T<1时,无病平衡解局部渐近稳定,此时疾病消亡;当T>1时,无病平衡解不稳定,此时系统存在唯一地方病平衡解,并在一定条件下证明了地方病平衡解的局部渐近稳定。
An age-structured SIS epidemic model with vertical transmission is discussed.With the assumption that the total population is invariant in the model,the basic reproduction number T which determines the extinction of epidemic disease is obtained.The disease-free equilibrium is locally asymptotically stable when the basic reproduction number T 1,that is to say the disease is extinct.The disease-free equilibrium is unstable when the basic reproduction number T 1,and a positive endemic solution appears which is also locally asymptotically stable under a certain condition.
出处
《石河子大学学报（自然科学版）》
CAS
2011年第5期649-654,共6页
Journal of Shihezi University(Natural Science)
基金
新疆大学自然科学基金项目(07020428010)
新疆大学偏微分方程精品课程建设项目
关键词
年龄结构
垂直传染
SIS传染病模型
基本再生数
平衡点
稳定性
age-structured
vertical transmission
epidemic model
basic reproduction number
equilibrium
stability
