一类具有非线性脉冲接种的SIRS流行病模型分析  

Analysis on an SIRS Epidemic Model with Nonlinear Pulse Vaccination

作　　者：李志民 张太雷[1] 高建忠 LI Zhimin;ZHANG Tailei;GAO Jianzhong(School of Science,Chang’an University,Xi’an,Shaanxi,710064,P.R.China)

机构地区：[1]长安大学理学院,西安陕西710064

出　　处：《数学进展》2020年第3期333-348,共16页Advances in Mathematics（China）

基　　金：the Fundamental Research Funds for the Central Universities,CHD(No.300102129202);Scientific Innovation Practice Project of Postgraduates of Chang’an University(No.300103002110);the Natural Science Basic Research Plan in Shaanxi Province of China(No.2018JM1011)and NSFC(No.11701041).

摘　　要：本文建立了一类具有非线性脉冲免疫接种与饱和接触率的SIRS传染病模型;利用离散动力系统的频闪映射方法得到了模型的无病周期解;利用Floquet乘子理论和脉冲微分方程比较定理证明了该周期解的全局渐近稳定性,并获得了模型持久性的充分条件;还通过数值模拟展示了数值模拟结果和理论结果的一致性.In this paper,we establish an SIRS epidemic model with pulse vaccination and saturated contact rate and nonlinear pulse immunization function.By using the stroboscopic map of discrete dynamical systems,the disease-free periodic solution(DFPS for short)of the model with impulsive vaccination is obtained.Based on the Floquet theory and comparison principle of impulsive differential equations,the global asymptotic stability of the DFPS is given,and the sufficient conditions for the permanence of the model are obtained.In addition,numerical simulations are done to illustrate our analytical results.

关 键 词：非线性脉冲接种 周期解 全局渐近稳定 持久性 

分 类 号：O175.1[理学—数学]