华东师范大学学报（自然科学版） ›› 2021, Vol. 2021 ›› Issue (3): 47-55.doi: 10.3969/j.issn.1000-5641.2021.03.006

• 数学 • 上一篇    下一篇

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   

  1. 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 出版日期:2021-05-25 发布日期:2021-05-26
  • 通讯作者: 聂麟飞 E-mail:512077753@qq.com;lfnie@163.com
  • 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   

  1. College of Mathematics and System Science, Xinjiang University, Urumqi　830046, China
  • Received:2020-01-19 Online:2021-05-25 Published:2021-05-26
  • Contact: Linfei NIE E-mail:512077753@qq.com;lfnie@163.com

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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.

关键词: 媒介传染病模型, 年龄结构与水平传播, 基本再生数, 无病和地方病平衡态, 稳定性与持久性

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.

Key words: vector-borne infectious disease model, age-structured and horizontal transmission, the basic reproduction number, disease-free and endemic equilibrium, stability and persistence

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