预防接种情况下具有非线性传染率的SEIR传染病模型的全局分析  

Global Analysis of a SEIR Epidemic Model with Nonlinear Incidence Rate under Vaccination

作　　者：朱慧[1,2] 熊佐亮[1] 王娓[1] 

机构地区：[1]南昌大学数学系,江西南昌330031 [2]北京理工大学珠海学院,广东珠海519085

出　　处：《南昌大学学报（理科版）》2009年第2期113-117,共5页Journal of Nanchang University(Natural Science)

基　　金：江西省自然科学基金资助项目(0611084)

摘　　要：研究一类具有预防接种的非线性传染率SEIR传染病模型,得到了各类平衡点存在的阈值条件。利用Lia-punov-Lasalle不变集原理证明了无病平衡点全局渐近稳定,利用Hurwitz判别法得到了地方病平衡点的局部渐近稳定的充分条件。应用微分方程轨道稳定和复合矩阵的相关理论得到了地方病平衡点的全局渐近稳定性的充分条件。The global analysis of a SEIR epidemic model with nonlinear incidence rate under vaccination is studied. The conditions and threshold to the existence of equilibriums are found. By Liapunov - Lasalle invariant theorem, the globally asymptotic stability of disease - free equilibrium is proved. By Hurwitz criterion, the sufficient condition of locally asymptotic stability of endemic equilibrium is obtained. And the sufficient condition under which endemic equilibrium is globally asymptotic stability is given by the theory about asymptotically orbital stability in differential equations and compound matrix.

关 键 词：预防接种 SEIR传染病模型 平衡点 全局渐近稳定性 

分 类 号：O175.1[理学—数学]