猴痘病毒传播的传染病动力学建模与定性分析

Infectious Disease Dynamics Modeling and Qualitative Analysis of Monkeypox Virus Transmission

摘要: 本文通过对猴痘病毒的传播机制的分析，并考虑了天花疫苗对猴痘病毒的交叉防护，构建了包含隔离措施和疫苗接种的SEIQVR猴痘病毒模型。通过应用下一代矩阵法，计算了模型的基本再生数$R_0=max\left\{R_{01},R_{02}\right\}$ ，其中人类种群的基本再生数为$R_{01}$ ，动物种群的基本再生数为$R_{02}$ ，并验证了相关的阈值定理。根据$R_{01}$ 和$R_{02}$ 的值，我们确定了三类平衡点的存在性，包括无病平衡点、无猴痘地方病平衡点及共存的地方病平衡点。利用Hurwitz判据，我们证明了这些平衡点的局部稳定性，并通过构造Lyapunov函数结合LaSalle不变性原理评估了其全局稳定性。数值模拟结果进一步验证了所得到结论的合理性。

Abstract: This study analyzes the transmission mechanism of the monkeypox virus and considers the cross-protection of the smallpox vaccine against monkeypox. We construct an SEIQVR monkeypox model that incorporates isolation measures and vaccination. By applying the next generation matrix method, we calculate the basic reproduction number $R_0=max\left\{R_{01},R_{02}\right\}$ , where $R_{01}$ is the basic reproduction number for the human population and $R_{02}$ is the basic reproduction number for the animal population, and we verify the related threshold theorem. Based on the values of $R_{01}$ and $R_{02}$ , we determine the existence of three types of equilibrium points: The disease-free equilibrium, the monkeypox endemic equilibrium, and the coexistence endemic equilibrium. Using the Hurwitz criterion, we prove the local stability of these equilibrium points and assess their global stability by constructing a Lyapunov function in conjunction with the LaSalle invariance principle. Numerical simulation results further validate the reasonableness of the conclusions obtained.