一类带有一般接触率和常数输入的流行病模型的全局分析  

Global Analysis of Some Epidemic Models With General Contact Rate and Constant Immigration

作　　者：李健全[1] 张娟[1] 马知恩[1] 

机构地区：[1]西安交通大学应用数学系

出　　处：《应用数学和力学》2004年第4期359-367,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(19971066)

摘　　要：　借助极限系统理论和构造适当的Liapunov函数,对带有一般接触率和常数输入的SIR型和SIRS型传染病模型进行讨论·　当无染病者输入时,地方病平衡点存在的阈值被找到·　对相应的SIR模型,关于无病平衡点和地方病平衡点的全局渐近稳定性均得到充要条件;对相应的SIRS模型,得到无病平衡点和地方病平衡点全局渐近稳定的充分条件·　当有染病者输入时,模型不存在无病平衡点·　对相应的SIR模型,地方病平衡点是全局渐近稳定的;对相应的SIRS模型。An epidemic models of SIR type and SIRS type with general contact rate and constant immigration of each class were discussed by means of theory of limit system and suitable Liapunov functions.In the absence of input of infectious individuals,the threshold of existence of endemic equilibrium is found.For the disease-free equilibrium and the endemic equilibrium of corresponding SIR model,the sufficient and necessary conditions of global asymptotical stabilities are all obtained.For corresponding SIRS model,the sufficient conditions of global asymptotical stabilitiese of the disease-free equilibrium and the endemic equilibrium are obtained.In the existence of input of infectious individuals,the models have no disease-free equilibrium.For corresponding SIR model,the endemic equilibrium is globally asymptotically stable;for corresponding SIRS model,the sufficient conditions of global asymptotical stability of the endemic equilibrium are obtained.

关 键 词：传染病模型 平衡点 全局渐近稳定性 极限系统 

分 类 号：O175.12[理学—数学]