一类SEIRQ模型的全局稳定性和分岔分析
Global stability and bifurcation analysis of a class of SEIRQ models
刘秋梅 1刘玲伶1
作者信息
- 1. 西南石油大学理学院,四川 成都 610050
- 折叠
摘要
研究了一类SEIRQ传染病模型的全局稳定性和分岔现象.基于基本再生数,给出了地方病平衡点的存在条件.讨论了无病平衡点和地方病平衡点的局部稳定性,进一步借助Li-Muldowney的几何方法讨论了地方病平衡点的全局稳定性,利用中心流形定理和正规形理论证明了模型发生了跨临界分岔的现象,展示了传染病在长期传播过程中会逐渐演变成地方传染疾病.最后,对模型进行了数值模拟验证了理论证明的结果.
Abstract
The global stability and bifurcation of a SEIRQ model of infectious disease are studied.Based on the basic re-production number,the endemic equilibrium's existence conditions are derived.The local stability conditions of the endemic and disease-free equilibrium are given.Moreover,the Li-Muldowney geometric technique is applied to study the global stability of endemic disease equilibrium.By the center manifold theorem and normal form theory,it is proved that the transcritical bi-furcation occurs,which shows that infectious diseases gradually evolve into endemic diseases during long-term transmission.Finally,the theoretical results are illustrated by numerical simulations.
关键词
传染病模型/全局稳定性/跨临界分岔/数值模拟Key words
epidemic model/global stability/transcritical bifurcation/numerical simulation引用本文复制引用
基金项目
国家自然科学基金项目(12171337)
四川省科技厅自然科学基金项目(2022NSFSC1834)
四川省科技厅自然科学基金项目(2022NSFSC0529)
出版年
2024
NETL
NSTL
万方数据