具有自我保护和隔离措施的传染病模型动力学分析

Dynamic Analysis of Epidemic Models with Self-Protection and Isolation Measures

摘要: 该文建立并分析具有自我保护和隔离措施的传染病动力学模型，通过计算基本再生数并构造Lyapunov函数讨论了模型平衡点的稳定性。证明了当R₀<1时，无病平衡点是全局渐近稳定的；当R₀>1时，地方病平衡点是全局渐近稳定的。利用重庆市2022年11月1日到11月25日的COVID-19病例数据进行拟合，根据数值分析得到：加强对感染者的隔离措施可以在一定程度上控制疫情，但是增强个体的自我保护措施可以更加有效地减少被感染的风险和控制疫情的传播，更利于实际应用。

Abstract: The paper develops and analyzes an epidemic dynamics model with self-protection and isolation measures, and discusses the stability of the model equilibrium point by calculating the basic re-generation number and constructing a Lyapunov function. It is proved that the disease-free equilib-rium point is globally asymptotically stable when R₀<1 ; when 当R₀>1 , the endemic equilibrium point is globally asymptotically stable. Using the data of COVID-19 cases from November 1 to No-vember 25, 2022 in Chongqing Municipality for fitting, according to the numerical analysis, we ob-tained that: strengthening the isolation measures for infected people can control the epidemic to a certain extent, but enhancing the self-protection measures of individuals can be more effective in reducing the risk of being infected and controlling the spread of the epidemic, which is more condu-cive to the practical application.