摘要
研究了一类潜伏期、染病期均传染且具有不同饱和接触率C1（N）和C2（N）的SEIS传染病模型,得到了疾病流行的基本再生数R0.运用Liapunov函数方法,证明了当R0〈1时,无病平衡点P0全局渐近稳定,疾病最终消失;利用Hurwitz判据定理,证明了当R0〉1时,P0不稳定,地方病平衡点P＊局部渐近稳定;当因病死亡率为零时,极限系统的地方病平衡点P＊全局渐近稳定.
A SEIS epidemic model with infective force in both latent period and infected period, having different general saturated contact rate C1 （N） and C2 （N）, is studied and the basic reproductive number R0 is obtained. By using Liapunov function method, it is proved that the disease-free equilibrium P0 is globally asymptotically stable and the disease always dies out eventually if R0〈1. It is also proved that in the case where R0〉1, P0 is unstable and the unique endemic equilibrium P＊ is locally asymptotically stable by Hurwitz criterion theory. It is shown that when disease-induced death rate is zero, the unique endemic equilibrium P＊ of the limiting system is globally asymptotically stable.
出处
《陕西师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2008年第6期5-9,共5页
Journal of Shaanxi Normal University：Natural Science Edition
基金
国家自然科学基金重点资助项目(10531030)
