井冈山大学学报（自然科学版）2025，Vol.46Issue(2)：1-8,8.DOI:10.3969/j.issn.1674-8085.2025.02.001
疫苗接种和传染率依赖于信息的传染病模型分析
ANALYSIS OF AN EPIDEMIC MODEL WITH INFORMATION DEPENDENT VACCINATION AND TRANSMISSION RATE
摘要
Abstract
In order to investigate the effect of information on vaccination and transmission rate,an SIR epidemic model was formulated.Firstly,the basic reproduction number R0 was given,which can be used to characterize the disease transmission dynamics,namely,if R0 ≤ 1,the disease dies out,if R0＞1,the disease persists and there is one unique endemic equilibrium.Secondly,the local stability of the endemic equilibrium and the existence of Hopf bifurcation was discussed.A Lyapunov function was constructed to study the global stability of the endemic equilibrium if vaccination is not information-related.When vaccination is information-related,a stability quantity which determines the stability of the periodic solution and the direction of bifurcation is obtained.Theoretical results indicate that sustained oscillations of disease can arise purely due to the information-related vaccination.Finally,numerical simulations are provided to show how the stability properties depend on the relevant parameters of the model.关键词
信息变量/接种/基本再生数/Lyapunov函数/Hopf分支Key words
information variable/vaccination/basic reproduction number/Lyapunov function/Hopf bifurcation分类
数学引用本文复制引用
刘飞燕,刘俊利..疫苗接种和传染率依赖于信息的传染病模型分析[J].井冈山大学学报（自然科学版）,2025,46(2):1-8,8.基金项目
国家自然科学基金项目(11801431) （11801431）
陕西省杰出人才项目(10701000506) （10701000506）
陕西省自然科学基础研究计划项目(2024JC-YBMS-001,2022JM-023) （2024JC-YBMS-001,2022JM-023）
