具有垂直传染的SIRS传染病模型分岔分析  

Bifurcation Analysis of an 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：《郑州大学学报（理学版）》2013年第2期31-36,共6页Journal of Zhengzhou University:Natural Science Edition

基　　金：国家自然科学基金资助项目;编号11162004;60964006;广西省自然科学基金资助项目;编号2012GXNSFAA053006;广西省研究生教育创新计划资助项目;编号YCSZ2012072

摘　　要：研究了一个具有脉冲生育、脉冲接种和垂直传染的SIRS传染病模型的动力学行为,其中,脉冲生育和脉冲接种发生在不同时刻,得到了决定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.进一步,数值模拟较好地验证了理论分析.The dynamical behaviors of an SIRS epidemic model with the effects of birth pulse, pulse vaccination and vertical transmission at different moments were studied. The threshold for a disease to be extinct or endemic was established. The Poincare map and center manifold theorem were used to discuss flip bifurcation of the endemic periodic solution. Numerical results for periodic solutions and bifurcation diagrams, which were illustrated with an example, were 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]