摘要
系统研究了具有急性和慢性两个阶段的MSIS流行病模型.由两节构成,第1节建立和研究了具有急慢性阶段的MSIS流行病模型;第2节在第1节的基础上建立和研究了具有慢性病病程的MSIS流行病模型.第1节的模型是四个常微分方程构成的方程组.第2节的模型既含有常微分方程,又含有偏微分方程.运用微分方程和积分方程中的理论和方法,得到了这两个模型再生数R0的表达式.证明了当R0<1时,无病平衡态是全局渐近稳定性,给出了各模型地方病平衡态的存在性和稳定性条件.
This paper considers an MSIS epidemic model with acute and chronic stages. It consists of two sections. Section 1 presents and analyzes an MSIS epidemic model with acute and chronic infection stages, which consists of ODEs; Section 2 studies an MSIS epidemic model with the age of chronic infection, which consists of ODEs and PDEs at the same time. Under the assumption of exponentially change of the total population, the explicit formula of the reproductive numbers R_0 for both models are obtained, the global stability of the disease-free equilibria and stability conditions of the endemic equilibria are given.
出处
《应用泛函分析学报》
CSCD
2005年第1期83-96,共14页
Acta Analysis Functionalis Applicata
基金
国家自然科学基金(10371105)
河南省杰出青年科学基金(0312002000)
关键词
流行病模型
病程结构
再生数
平衡点
稳定性
急慢性阶段
常微分方程
acute and chronic infection stages
MSIS epidemic models
age of chronic infection
reproductive number
steady states
stability
