具垂直传染的SIRS传染病模型的脉冲控制和分岔分析  

Pulse Control and Bifurcation Analysis of a SIRS Epidemic Model with Vertical Transmission

作　　者：郝丽杰[1] 蒋贵荣[1] 鹿鹏[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《广西师范大学学报（自然科学版）》2012年第4期42-47,共6页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11162004;60964006);广西自然科学基金资助项目(2012GXNSFAA053006)

摘　　要：本文研究一个具有脉冲生育、脉冲接种和垂直传染的SIRS传染病模型的动力学行为,给出超临界分岔发生的条件,得到了疾病流行与否的阈值。通过利用Poincaré映射和中心流形定理,讨论了地方病周期解的flip分岔,并给出能验证理论分析的数值结果。In this paper,the dynamical behavior of a SIRS epidemic model with birth pulse,pulse vaccination and vertical transmission are studied. The condition of existence for supercritical bifurcation is derived,and then the threshold for a disease to be extinct or endemic is established. The Poincar6 map and center manifold theorem are used to discuss flip bifurcation of endemic periodic solution. Numerical results for periodic solutions and bifurcation diagrams ,which are illustrated with an example ,are in good agreement with the theoretical analysis.

关 键 词：SIRS传染病模型 垂直传染 脉冲接种 阈值 分岔 

分 类 号：O175.1[理学—数学]