摘要
研究一类具有一般形式非线性饱和传染率染病年龄结构SIS流行病传播数学模型动力学性态,得到疾病绝灭和持续生存的阈值条件――基本再生数。当基本再生数小于或等于1时,仅存在无病平衡点,且在其小于1的情况下,无病平衡点全局渐近稳定,疾病将逐渐消除;当基本再生数大于1时,存在不稳定的无病平衡点和唯一的局部渐近稳定的地方病平衡点,疾病将持续存在。已有的两类模型可视为本模型的特例,其相关结论可作为本文的推论。
Dynamical behavior of an infection-age-dependent SIS epidemic model with general form nonlinear saturated infectivity is studied and the threshold, a basic reproductive number which determines the outcome of the infectious disease is found. When the basic reproductive number is not greater than 1 meaning the disease will be extinct, there exists only a disease-free equilibrium, which is globally asymptotically stable except that the basic reproductive number equals 1. When the basic reproductive number is greater than 1 meaning the disease will persist, there are two equilibria, the disease-free equilibrium which is unstable and the endemic equilibrium which is locally asymptotically stable. The previous ODE model can be viewed as especial example and its relevant results can be regarded as corollaries of this article.
出处
《工程数学学报》
CSCD
北大核心
2005年第5期929-934,共6页
Chinese Journal of Engineering Mathematics
基金
Supported by the National Natural Science Foundation of China (10371097).
