摘要
讨论一类具有常数输入且传染率为非线性的SEIS流行病传播数学模型,给出了决定疾病灭绝和持续生存的基本再生数R_0.当R_0<1时,无病平衡点全局渐近稳定;当R_0>1时,利用第二加性复合矩阵证明了惟一地方病平衡点全局渐近稳定.
An epidemic model with constant input and nonlinear incidence rate is investigated in this paper, and the basic reproductive number R0 which determines the outcome of the infections disease is found. The disease-free equilibrium is globally asymptotical stable when R0 〈 1. Using second additive compound matrix, it is proved that the unique endemic equilibrium is globally asymptotical stable when R0 〉 1.
出处
《高校应用数学学报（A辑）》
CSCD
北大核心
2009年第1期53-57,共5页
Applied Mathematics A Journal of Chinese Universities(Ser.A)
关键词
传染病模型
非线性传染率
基本再生数
全局渐近稳定性
epidemic model
nonlinear incidence rate
basic reproductive number
global asymptotical stability
