具有饱和发生率的多斑块传染病模型的动力学分析
Dynamic analysis of a multi-patch epidemic model with saturated incidence rate
李宇航 1刘茂省2
作者信息
- 1. 中北大学数学学院,030051,山西省太原市
- 2. 中北大学数学学院,030051,山西省太原市;北京建筑大学理学院,102616,北京市
- 折叠
摘要
建立了一类斑块环境下具有饱和发生率的SVEIQR传染病模型,该模型考虑了疫苗接种和隔离策略.首先,通过构造再生矩阵得到了基本再生数R.的矩阵表示.然后,应用Lyapnuov函数法证明了当R0＜1时无病平衡点的全局渐近稳定性.最后,对R0进行了敏感性分析和数值模拟.结果表明:增加接种率和隔离率都能够减少基本再生数的大小;人口从高风险地区到低风险地区迁移率增加能够增大基本再生数的值.所以,当疾病爆发后,应严格控制高风险地区的人口向外流动,并及时进行疫苗接种以及采取相应的隔离策略.
Abstract
A SVEIQR epidemic model with saturated incidence in a patch environment that incorpo-rates vaccination and quarantine strategies is proposed.Firstly,the matrix representation of the basic re-production number R0 through the construction of the reproduction matrix is obtained.Next,we apply the Lyapunov function method to demonstrate that the global asymptotic stability of the disease-free equilibri-um.Finally,we validate our theoretical results through numerical simulations and carry out sensitivity a-nalysis of R0.Our findings demonstrate that increasing the vaccination rate and quarantine rate can reduce the basic reproduction number;the increase of population migration from high-risk areas to low-risk areas can increase the value of the basic reproduction number.Therefore,after the outbreak of the disease,it is necessary to strictly control the outward flow of population in high-risk areas,and timely vaccination and quarantine strategies should be implemented.
关键词
饱和发生率/斑块/SVEIQR传染病模型/稳定性分析Key words
saturated incidence rate/patch/SVEIQR epidemic model/stability analysis引用本文复制引用
基金项目
国家自然科学基金(12071445)
国家自然科学基金(12001501)
出版年
2024
国家科技期刊平台
NSTL
维普
万方数据