具有疫苗接种和自我防护行为的年龄结构MSVEIR传染病模型的稳定性分析

Analyzing the Stability of an Age-Structured MSVEIR Epidemic Model Incorporating Vaccination and Self-Protection

摘要: 本文建立了一类具有疫苗接种和自我防护行为的年龄结构MSVEIR流行病模型。利用算子半群理论证明了模型解的存在唯一性，通过特征方程推导出基本再生数${ℛ}_0$ 的表达式，并研究了无病平衡点和地方病平衡点的存在性和稳定性。证明了当${ℛ}_0<1$ 时，无病平衡点是全局渐近稳定的；当${ℛ}_0>1$ 时，地方病平衡点是局部渐近稳定的。同时用基本再生数${ℛ}_0$ 的表达式进一步解释了接种在控制消除传染病中的作用。

Abstract: This paper establishes an age-structured MSVEIR epidemic model incorporating vaccination and self-protection behaviors. By employing operator semigroup theory, we establish the existence and uniqueness of the solutions of the model. The expression for the basic reproduction number is derived via the characteristic equation, and the existence and stability of both the disease-free equilibrium and the endemic equilibrium are rigorously analyzed. Specifically, we prove that the disease-free equilibrium is globally asymptotically stable when ${ℛ}_0<1$ , while the endemic equilibrium is locally asymptotically stable when ${ℛ}_0>1$ . Furthermore, the role of vaccination in the control and elimination of infectious diseases is further elucidated through the analytical expression of ${ℛ}_0$ .