具有阶段结构的SIR传染病模型  

A SIR Epidemic Model with Stage Structure

作　　者：朱慧[1,2] 熊佐亮[1] 李顺异[1] 赵宇[3] 

机构地区：[1]南昌大学数学系,江西南昌330047 [2]淮阴工学院计算科学系,江苏淮安223002 [3]清华大学数学科学系,北京100084

出　　处：《应用泛函分析学报》2008年第4期352-359,共8页Acta Analysis Functionalis Applicata

基　　金：江西省自然科学基金(0611084)

摘　　要：研究了一类具有阶段结构的SIR传染病模型,在模型中假设种群分幼年和成年两个阶段,且只有成年种群染病.并且采用与成年易感者数量有关的一般非线性传染率,得到了系统解的有界性及无病平衡点和地方病平衡点存在的条件.通过对平衡点对应的特征方程的讨论得到了平衡点局部渐近稳定的条件,同时证明了平衡点的全局渐近稳定性,并对结论进行了数值模拟.A SIR epidemic model with stage structure is studied in this paper. The immature, mature stage and a nonlinear infective rate related to mature individuals are considered. It is assumed that only the mature individuals can be infected. The boundness of solution and the existence of the disease-free equilibrium and endemic equilibrium are obtained. The conditions of locally asymptotic stability of equilibriums are obtained by discussing the eigenvalue equation of the equilibriums. Furthermore, the globally asymptotic stability of equilibriums is proved. And the numerical simulation is given.

关 键 词：阶段结构 SIR传染病模型 平衡点 稳定性 

分 类 号：O175.1[理学—数学]