| 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].井冈山大学自然版,2025,46(2):1-8 |
| 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 |
| 投稿时间：2024-11-13 修订日期：2024-12-24 |
| DOI：10.3969/j.issn.1674-8085.2025.02.001 |
| 中文关键词: 信息变量 接种 基本再生数 Lyapunov函数 Hopf分支 |
| 英文关键词: information variable vaccination basic reproduction number Lyapunov function Hopf bifurcation |
| 基金项目:国家自然科学基金项目(11801431)；陕西省杰出人才项目(10701000506)；陕西省自然科学基础研究计划项目(2024JC-YBMS-001,2022JM-023) |
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| 中文摘要: |
| 为了研究信息对接种率和传染率的影响，建立了一个 SIR 传染病模型。首先给出了模型的基本再生数R0，证明了疾病的传播动力学可由基本再生数来刻画，即当 R0 ≤1 时，疾病绝灭；当 R0 > 1时，疾病持久存在，且模型存在唯一的地方病平衡点。其次讨论了地方病平衡点的局部稳定性和 Hopf 分支的存在性。通过构造Lyapunov 函数，研究了当接种不依赖于信息变量时，地方病平衡点的全局稳定性；当接种依赖于信息变量时，只给出了一个决定周期解稳定性和分支方向的量。理论分析表明疾病的持续震荡，可能完全是由于这种与信息相关的疫苗接种而引起的。最后，利用数值模拟研究了模型相关参数对于稳定性的影响。 |
| 英文摘要: |
| 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. |
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