具有时滞和类年龄结构的媒介传染病模型研究  

Study on a vector-borne epidemic model with time-delay and age structure

作　　者：刘慧慧 王雅萍 聂麟飞[1] LIU Huihui;WANG Yaping;NIE Linfei(College of Mathematics and System Science,Xinjiang University,Urumqi 830017,China)

机构地区：[1]新疆大学数学与系统科学学院,乌鲁木齐830017

出　　处：《华中师范大学学报(自然科学版)》2025年第2期169-178,共10页Journal of Central China Normal University:Natural Sciences

基　　金：国家自然科学基金项目(12361103);新疆维吾尔自治区自然科学基金项目(2022TSYCCX0015,2021D01E12).

摘　　要：该文基于疫苗接种年龄、潜伏期年龄以及时滞效应对疾病传播的潜在影响,构建了一类兼具时滞特性与类年龄结构的媒介传染病模型.首先,推导了基本再生数R_(0)的精确表达式,并借助它对各类平衡态的存在性进行了系统刻画.进一步,构造合适的Lyapunov函数分析无病平衡态的稳定性,当R_(0)<1时无病平衡态是全局渐近稳定的;当R_(0)>1时,地方病平衡态是存在的并且疾病将持续存在.最后,通过数值模拟对主要的理论成果进行了解释.Based on the potential influence of vaccination age and latency age as well as the effect of time delay on the transmission of the disease,a kind of age-structured vector-borne infectious disease model with time delay is constructed in this paper.Firstly,the exact expression of the basic reproduction number R_(0) is drived,and the existence of various steady states is systematically characterised with it.Further,a suitable Lyapunov function is constructed to analyze the stability of disease-free steady state.The disease-free steady state is globally asymptotically stable when R_(0)<1,while the endemic steady state exists and the disease is consistently persistent when R_(0)>1.Finally,numerical simulations are used to explain the main theoretical results.

关 键 词：疫苗接种年龄 潜伏年龄 基本再生数 稳定性 一致持续性 

分 类 号：O175[理学—数学]