具有标准发生率和脉冲干扰的SIRS模型稳定性分析

Stability Analysis of an SIRS Model With Standard Incidence and Impulsive Perturbations

本文同时考虑脉冲接种和脉冲剔除策略,建立一个具有标准发生率的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,得到模型无病T周期解的存在性和疾病流行与否的阈值-基本再生数R_0;其次,应用Floquet定理证明了无病T周期解是局部渐近稳定的;然后,利用脉冲微分不等式证明了无病T周期解是全局渐近稳定的;最后,进行计算机数值模拟来进一步验证理论结果的正确性。

In this paper, impulsive vaccination and impulsive elimination 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, the disease - free T periodic solution and the threshold, basic reproductive number R0 which determines whether a disease is extinct or not , are ob- tained. Secondly, the disease - free T periodic solution is locally asymptotically stable by Floquet theorem. Thirdly, the disease - free T periodic solution is globally asymptotically stable by impulsive differention in equation. Finally, numerical simulation is given to illustrate the theoretical analysis.