TWO DIFFERENTIAL INFECTIVITY EPIDEMIC MODELS WITH NONLINEAR INCIDENCE RATE  

作　　者：Chen Junjie 

机构地区：[1]Dept. of Math. ,Zhejiang Univ. ,Hangzhou 310027,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2005年第3期305-315,共11页高校应用数学学报（英文版）（B辑）

基　　金：SupportedbytheScienceFoundationoftheEducationDepartmentofZhejiangProvince

摘　　要：This paper considers two differential infectivity（DI） epidemic models with a nonlinear incidence rate and constant or varying population size. The models exhibits two equilibria, namely., a disease-free equilibrium O and a unique endemic equilibrium. If the basic reproductive number σ is below unity,O is globally stable and the disease always dies out. If σ〉1, O is unstable and the sufficient conditions for global stability of endemic equilibrium are derived. Moreover,when σ〈 1 ,the local or global asymptotical stability of endemic equilibrium for DI model with constant population size in n-dimensional or two-dimensional space is obtained.This paper considers two differential infectivity（DI） epidemic models with a nonlinear incidence rate and constant or varying population size. The models exhibits two equilibria, namely., a disease-free equilibrium O and a unique endemic equilibrium. If the basic reproductive number σ is below unity,O is globally stable and the disease always dies out. If σ〉1, O is unstable and the sufficient conditions for global stability of endemic equilibrium are derived. Moreover,when σ〈 1 ,the local or global asymptotical stability of endemic equilibrium for DI model with constant population size in n-dimensional or two-dimensional space is obtained.

关 键 词：differential infectivity nonlinear incidence rate endemic equilibrium global stability Liapunov function. 

分 类 号：R51[医药卫生—内科学] O29[医药卫生—临床医学]