摘要
根据染病者在不同阶段具有不同的传染力以及不同阶段的染病者可以转化的特性,建立了一类带有阶段结构的传染病传播模型。借助再生矩阵求得了所建模型的基本再生数,并应用极限系统理论证得:当基本再生数不超过1时,模型仅存在全局稳定的无病平衡点;当基本再生数大于1时,无病平衡点不稳定,而且存在渐近稳定的地方病平衡点,当不考虑因病死亡率时,地方病平衡点是全局渐近稳定的。
According to the specialty of infection transmission that infected individuals have different infectivities in different stages and that infected individuals can move from a stage into the other stage with the development of infection, an epidemic model with stage is established. The basic reproduction number is found by means of the next generation matrix. By applying the theory of asymptotically autonomous systems, the following results are obtained ： the disease- free equilibrium is globally asymptotically stable when the basic reproduction number is not greater than 1 ; the endemic equilibrium is locally asymptotically stable when the basic reprod.uction number is greater than 1. When the disease is not fatal, the endemic equilibrium is globally asymptotically stable if it exists.
出处
《空军工程大学学报（自然科学版）》
CSCD
北大核心
2008年第1期86-88,共3页
Journal of Air Force Engineering University(Natural Science Edition)
基金
国家自然科学基金资助项目(10671209
30670486)
关键词
传染病模型
基本再生数
稳定性
阶段结构
epidemic model
basic reproduction number
stability
stage structure
