数学

具有年龄结构和水平传播的媒介传染病模型研究

  • 梁霜霜 ,
  • 聂麟飞 ,
  • 胡琳
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  • 新疆大学 数学与系统科学学院, 乌鲁木齐 830046

收稿日期: 2020-01-19

  网络出版日期: 2021-05-26

基金资助

国家自然科学基金(1961066, 11771373); 新疆维吾尔自治区高校科研计划(XJEDU2018I001)

Analysis of vector-borne infectious disease model with age-structured and horizontal transmission

  • Shuangshuang LIANG ,
  • Linfei NIE ,
  • Lin HU
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  • College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China

Received date: 2020-01-19

  Online published: 2021-05-26

摘要

考虑到病毒变异和感染年龄的普遍存在性, 提出了一类具有潜伏年龄和水平传播的媒介-宿主传染病模型, 给出了基本再生数 ${\cal R}_0$ 的精确表达式, 刻画了该模型无病平衡态和地方病平衡态的存在性. 进一步, 利用线性近似方法和构造合适的Lyapunov函数及LaSalle不变原理等方法, 证明了当 ${\cal R}_0<1$ 时, 无病平衡态 ${\cal E}_{0}$ 是全局渐近稳定的, 疾病也最终趋于灭绝; 而当 ${\cal R}_0>1$ 时, 地方病平衡态是全局渐近稳定的, 疾病将持续下去而形成地方病.

本文引用格式

梁霜霜 , 聂麟飞 , 胡琳 . 具有年龄结构和水平传播的媒介传染病模型研究[J]. 华东师范大学学报(自然科学版), 2021 , 2021(3) : 47 -55 . DOI: 10.3969/j.issn.1000-5641.2021.03.006

Abstract

Considering the prevalence of variations in virus strains and the age of infection, a vector-borne infectious disease model with latent age and horizontal transmission is proposed. An exact expression for the basic reproduction number, ${\cal R} _0 $ , is given, which characterizes the existence of the disease-free equilibrium and the endemic equilibrium for this model. Next, by using a combination of linear approximation methods, constructing suitable Lyapunov functions, LaSalle invariance principles, and other methods, we prove that if ${\cal R}_0 <1 $ , then the disease-free equilibrium has global asymptotic stability, and the disease will eventually become extinct; if ${\cal R}_0>1$ , then the endemic equilibrium is globally asymptotically stable, and the disease will continue to form an endemic disease.

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