一类带有阶段结构的传染病模型的定性分析  

Qualitative Analysis of an Epidemic Model with Stage Structure

作　　者：杨建雅[1] 张凤琴[1] 杨友社[2] 

机构地区：[1]运城学院应用数学系,山西运城044000 [2]空军工程大学应用数学物理系,西安710051

出　　处：《数学的实践与认识》2007年第17期83-88,共6页Mathematics in Practice and Theory

基　　金：山西省自然科学基金项目(2005Z010);山西省重点扶持学科项目;运城学院项目(2005207);空军工程大学理学院科研基金项目

摘　　要：通过假设被感染者恢复后不具有免疫力,但易感性不同于未被感染过的易感者,建立了一类带有双线性传染率的传染病模型,发现该模型对一定参数会发生后向分支,找到了相应的阈值,完整分析了该模型的动力学性态.By assuming that the infectives have no immunity after recovery from the disease and that their susceptibility is different from other susceptible individuals, an epidemic model with bilinear incidence rate was established. It was found that backward bifurcation occurs for some parameters. The associated thresholds were determined, and the dynamical behivor was investigated completely.

关 键 词：传染病模型 后向分支 稳定性 

分 类 号：O193[理学—数学]