一类具有非线性发生率的带时滞的SIR传染病模型的局部渐近稳定性(英文)  

The Local Asymptotic Stability of an SIR Epidemic Model with Nonlinear Incidence Rate and Time Delay

作　　者：宋美[1] 刘广臣[1] 郭洪霞[1] 

机构地区：[1]鲁东大学数学与信息学院,山东烟台264025

出　　处：《生物数学学报》2011年第2期255-262,共8页Journal of Biomathematics

基　　金：A Project of Shandong Province Higher Educational Science and Technology Program (J09LA51);Supported by Program for Innovative Research Team in Ludong University(08-CXB005)

摘　　要：基于传统的SIR传染病模型,本文提出了一类具有非线性发生率的带时滞的传染病模型,得出了当S_0<T=(μ_2+λ)/β,对任意的时间滞后h,无病平衡点E_0是局部渐近稳定的;当S_0>(μ_2+λ)/β,无病平衡点E_0是不稳定的,此时,正平衡点E_+是局部渐近稳定的.In this paper, based on a famous SIR epidemic model, we propose a class of revised SIR epidemic model with time delay. In this model with nonlinear incidence rate, the birth rate of population depends on the density of population. According to the well known Roth-Hurwitz criterion, we show that, if So 〈 T = μ2＋λ/β , the disease free equilibrium E0 is locally asymptotically stable for any time delay h. If So 〉 μ2＋λ/β, E0 is unstable for any time delay h. If So 〉 T = μ2＋λ/β, then the endemic equilibrium E＋ is locally asymptotically stable for any time delay h.

关 键 词：SIR传染病模型 时间滞后 局部渐近稳定性 功能性反应函数 

分 类 号：O175.13[理学—数学]