具有饱和感染率的脉冲控制SIR 模型的全局动力学分析

摘要：

研究了一类具有饱和感染率的状态依赖脉冲控制的 SIR 模型,给出了基础模型平衡点的具体表达式及其稳定性的条件,讨论了具有脉冲控制的模型的无病周期解的存在性和全局稳定性,分析了 Poincaré 映射的性质,然后讨论了无病周期解处的分岔现象,最终通过数值模拟,验证了结论的正确性.

A state-dependent impulsive control SIR model with a saturated infection rate is studied. The expression for the equilibrium points of the base model and the conditions for their stability are given. The existence and global stability of the disease-free periodic solution of the model with impulsive control are discussed. The properties of the Poincaré map are analyzed, and the bifurcation phenomena at the disease-free periodic solution are examined. Finally, the correctness of the conclusions is verified through numerical simulations.

作者:

谢栋梁，焦彩霞，黄嵩，李永凤

Xie Dongliang, Jiao Caixia, Huang Song, Li Yongfeng

机构地区：

郑州轻工业大学数学与信息科学学院,

引用本文：

谢栋梁，焦彩霞，黄嵩等。具有饱和感染率的脉冲控制 SIR 模型的全局动力学分析[ ] ].河南师范大学学报(自然科学版),2025,53(5):97-104.(Xie Dongliang, Jiao Caixia, Huang Song,et al.Dynamic analysis of a state-de-pendent feedback control SlR model with saturation incidence[ ] ].Journal of Henan Normal University( Natural Science Edition),2025,53(5)97-104.D01：10.16366/j.cnki.1000-2367.2024.07.27.0002.)

基金：

国家自然科学基金；河南省自然科学基金

关键词：

传染病；SIR模型；饱和感染率；脉冲疫苗接种；分岔

infectious diseases; SIR model; saturation infection rate; pulse vaccination; bifurcation

分类号：

O175.2

具有饱和感染率的脉冲控制SIR 模型的全局动力学分析.pdf