摘要
研究了一个具有标准发生率、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性的条件;接着详细讨论了系统从平凡解到无病周期-1解的跨临界分岔现象,以及从无病周期-1解到无病周期-2解的flip分岔现象;最后给出了能很好地验证理论分析的数值结果.
The complex dynamics of an SIRS epidemic model with standard incidence, birth pulse, pulse vaccination and vertical transmission was investigated. First, a Poincare map was constructed, 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 transcritical bifurcation of the trivial solution and flip bifurcation of the infection-free period-1 solution of this model were discussed in detail. Finally, numerical results, which are in good agreement with the theoretical analysis, are presented.
出处
《中北大学学报（自然科学版）》
CAS
北大核心
2013年第4期367-371,共5页
Journal of North University of China(Natural Science Edition)
基金
国家自然科学基金资助项目(11162004)
广西省自然科学基金资助项目(2012GXNSFAA053006)
广西省研究生教育创新计划项目(YCSZ2012072)
关键词
SIRS模型
标准发生率
无病周期解
跨临界分岔
flip分岔
SIRS epidemic model
standard incidence
infection-free periodic solution
transcritical bifurcation
flip bifurcation
