一类具有双垂直传播和媒介呈Logistic增长的媒介传染病模型  

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

作　　者：李璐 张瑞霞[1] LI Lu;ZHANG Ruixia(School of Mathematics,North University of China,Taiyuan 030051,Shanxi,China)

机构地区：[1]中北大学数学学院,山西太原030051

出　　处：《山东大学学报(理学版)》2025年第4期93-103,共11页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(12001501,12071445)。

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R_(0),分析模型平衡点的存在性与全局稳定性。结果显示,当R_(0)<1时,无病平衡点全局渐近稳定;当R_(0)>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。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 R_(0)<1,the disease-free equilibrium is globally asymptotically stable,and when R_(0)>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.

关 键 词：媒介传染病 稳定性 双垂直传播 LOGISTIC增长 生物防治 

分 类 号：O175[理学—数学]