具有标准发生率和脉冲干扰的SIRS传染病模型分岔分析

The Bifurcation Analysis of an SIRS Epidemic Model with Standard Incidence and Impulsive Perturbations

本文同时考虑生育脉冲、垂直传染和脉冲治疗,建立一个带有标准发生率的SIRS传染病模型,从理论分析和数值模拟方面研究了SIRS传染病模型的动力学性质.首先利用Floquet乘子理论,证明了系统的平凡解、无病周期解和地方病周期解的存在性和稳定性;接着利用庞加莱映射、中心流形定理和分岔理论详细讨论了跨临界分岔和flip分岔,而且给出了能很好验证理论分析的数值结果;最后给出了生物学的解释和主要的结论.

Birth pulse,vertical transmission,and pulse treatment are considered in an SIRS model. The dynamical behavior of an SIRS epidemic model with standard incidence is discussed by means of both theoretical and numerical ways.Firstly,by using Floquet theory,the existence and stability of the trivial solution,infection-free periodic solution,and epidemic periodic solution are proved. Secondly,the Poincare map,center manifold theorem,and bifurcation theorem are used to discuss transcritical bifurcation and flip bifurcation.The numerical results,which are illustrated with an example,are in good agreement with the theoretical analysis. Finally,biological explanations and main conclusions are given.