山西大学学报（自然科学版）2025，Vol.48Issue(3)：445-455,11.DOI:10.13451/j.sxu.ns.2023159
有限医疗资源影响下的多尺度传染病模型研究
Analysis of Multi-scale Infectious Disease Model Under the Influence of Limited Medical Resources
摘要
Abstract
Considering the influence of the viral load in the host and limited medical resources on the transmission of infectious dis-eases,a multi-scale infectious disease model with saturated treatment rate coupling within-host and between-host dynamics is pro-posed.Firstly,for the between-host disease transmission model,the basic reproduction number is obtained,and a criterion describing the existence and stability of the disease-free and endemic equilibrium for the coupled model is given.Particularly,when the basic re-production number is less than 1,the model has two endemic equilibria,one of which is locally asymptotically stable and the other is unstable.When the basic reproduction number is greater than 1,the model has a unique endemic equilibrium,which is global asymp-totically stable under specific conditions.In addition,The existence of forward/backward bifurcation caused by limited medical re-sources is analyzed.This means that the elimination or prevalence of the disease no longer depends on the basic reproduction num-ber but is closely related to the initial state of infected humans and the supply of medical resources.Finally,the main theoretical re-sults of this paper are explained by numerical simulation.关键词
多尺度传染病模型/基本再生数/平衡点/渐近稳定性/前向/后向分支Key words
multi-scale infectious disease model/basic reproduction number/equilibrium/asymptotic stability/forward/backward bi-furcation分类
数学引用本文复制引用
王妙,王雅萍,聂麟飞..有限医疗资源影响下的多尺度传染病模型研究[J].山西大学学报（自然科学版）,2025,48(3):445-455,11.基金项目
国家自然科学基金(11961066) （11961066）
新疆维吾尔自治区自然科学基金(2021D01E12 （）
2021D01C070) （）
