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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (4): 50-59.doi: 10.6040/j.issn.1671-9352.0.2024.356

• • 上一篇    

具有周期感染率的年龄结构传染病模型的阈值动力学分析

董颖,吕云飞*   

  1. 天津工业大学数学科学学院, 天津 300387
  • 发布日期:2025-04-08
  • 通讯作者: 吕云飞(1984— ),男,教授,博士生导师,博士,研究方向为微分方程与动力系统. E-mail:lvyunfei@tiangong.edu.cn
  • 作者简介:董颖(2001— ),女,硕士研究生,研究方向为微分方程与生物数学. E-mail:dyingdydy@163.com*通信作者:吕云飞(1984— ),男,教授,博士生导师,博士,研究方向为微分方程与动力系统. E-mail:lvyunfei@tiangong.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(12471468);天津市自然科学基金资助项目(23JCZDJC00470)

Threshold dynamics analysis of an age-structured epidemic model with periodic infection rate

DONG Ying, LYU Yunfei*   

  1. School of Mathematical Sciences, Tiangong University, Tianjin 300387, China
  • Published:2025-04-08

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摘要： 本文研究了一类具有周期感染率和人口流动的年龄结构SEIR传染病模型。首先证明了模型非负解的存在唯一性。其次利用算子不动点定理和周期更新定理证明了模型地方病周期解的存在性和无病周期解的全局渐近稳定性。通过引入周期解算子在0点的Fréchet导数F〓的谱半径r(F〓),证明了当r(F〓)>1时, 模型存在地方病周期解(疾病爆发); 当r(F〓)<1时, 无病周期解是全局渐近稳定的(疾病灭绝)。

关键词: 年龄结构, 人口流动, 疫苗接种, 周期感染率, 周期解

Abstract: This paper studies an age-structured SEIR epidemic model with periodic infection rate and population flows. Firstly, the existence and uniqueness of non-negative solution of the model are proved. Subsequently, by using the operator fixed-point theorem and the periodic renewal theorem, the existence of endemic periodic solution and the global asymptotic stability of the disease-free periodic solution of the model are demonstrated. By introducing the spectral radius r(F )of the Fréchet derivative F of the periodic solution operator at point 0, it is shown that when r(F )>1, the model has an endemic periodic solution(disease outbreak); when r(F )<1, the disease-free periodic solution is globally asymptotically stable(disease extinction).

Key words: age structure, population mobility, vaccination, periodic infection rate, periodic solution

中图分类号: 

  • O175
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