具有饱和接触率和垂直传染的SIRS传染病模型分岔分析  

Bifurcation Analysis of a SIRS Epidemic Model with Saturating Contact Rate and Vertical Transmission

作　　者：凌琳[1] 刘苏雨[1] 蒋贵荣[1] 

机构地区：[1]桂林电子科技大学数学与计算科学学院,桂林541004

出　　处：《数学物理学报（A辑）》2014年第6期1415-1425,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11162004);广西自然科学基金(2012GXNSFAA053006);广西研究生教育创新计划项目(YCSZ2012072)资助

摘　　要：研究了一类具有饱和发生率、脉冲生育、脉冲接种和垂直传染的SIRS传染病模型的复杂动力学行为,首先构造了一个庞卡莱映射,然后利用映射的不动点及其特征值,得到了系统无病周期解的存在和稳定的条件,接着详细讨论了系统的跨临界分岔、超临界分岔和倍周期分岔现象,最后给出了能很好验证理论分析的数值结果.The complex dynamics of a SIRS epidemic model with saturate incidence rate, birth pulse, pulse vaccination and vertical transmission was studied. First, a Poincare map was formulated, the existence and stability of the infection-free periodic solution were obtained with the help of the fixed point of the map and its eigenvalues. Then transcritieal bifurcation, supercritical bifurcation and flip bifurcation were discussed in detail. Finally, numerical results, which are in good agreement with the theoretical analysis, were presented.

关 键 词：SIRS模型 饱和发生率 超临界分岔 跨临界分岔 倍周期分岔 

分 类 号：O175.1[理学—数学]