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《山东大学学报(理学版)》 ›› 2025, Vol. 60 ›› Issue (4): 93-103.doi: 10.6040/j.issn.1671-9352.0.2023.442

• • 上一篇    

一类具有双垂直传播和媒介呈Logistic增长的媒介传染病模型

李璐,张瑞霞*   

  1. 中北大学数学学院, 山西 太原 030051
  • 发布日期:2025-04-08
  • 通讯作者: 张瑞霞(1980— ),女,副教授,博士,研究方向为生物数学. E-mail:zhangruixia@nuc.edu.cn
  • 作者简介:李璐(1999— ),女,硕士研究生,研究方向为生物数学. E-mail:852373914@qq.com*通信作者:张瑞霞(1980— ),女,副教授,博士,研究方向为生物数学. E-mail:zhangruixia@nuc.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(12001501,12071445)

A vector-borne diseases model with dual vertical transmission and Logistic growth for vector

LI Lu, ZHANG Ruixia*   

  1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China
  • Published:2025-04-08

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摘要： 媒介传染病是通过生物媒介传播的传染性疾病,蚊媒传染病最为常见。本文考虑宿主和媒介的双垂直传播以及媒介Logistic增长,建立媒介传染病传播模型,求出基本再生数R0,分析模型平衡点的存在性与全局稳定性。结果显示,当R0<1时,无病平衡点全局渐近稳定;当R0>1时,正平衡点全局渐近稳定。最后通过数值模拟验证结论,同时揭示媒介呈Logistic增长时,如果不捕杀蚊虫,媒介传染病始终流行,当蚊虫灭杀率达到一定比例时,媒介传染病逐渐消亡,提高对蚊子的灭杀率会对传染病防治产生积极影响。

关键词: 媒介传染病, 稳定性, 双垂直传播, Logistic增长, 生物防治

Abstract: Vector-borne diseases are infectious diseases transmitted by vectors, and mosquito-borne diseases are the most common. Considering the dual vertical transmission of host and vector and Logistic growth for vector, the authors establish a vector-borne disease transmission model, calculate the basic reproduction number, analyze the existence and global stability of the equilibrium points, and show that when R0<1, the disease-free equilibrium is globally asymptotically stable, and when R0>1, the positive equilibrium is globally asymptotically stable. Finally, the numerical simulation verifies the conclusion, and reveals that when the vector is growing with Logistic, if the mosquito is not killed, the vector-borne disease is always present, and when the mosquito killing rate reaches a certain proportion, the vector-borne disease would eventually die out, and improving the killing rate of mosquitoes will have a positive impact on the prevention and control of infectious diseases.

Key words: vector-borne diseases, stability, dual vertical transmission, Logistic growth, biocontrol

中图分类号: 

  • O175
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