一类带有环境病毒量和疫苗影响的传染病模型平衡点的分析

Analysis of Equilibrium Points of a Class of Infectious Disease Models with Environmental Viral Load and Vaccine Effects

摘要: 本文研究了一类带有环境病毒量和疫苗影响的SLEIRVW传染病动力学模型，对模型进行了深入的动力学分析和计算，通过下一代矩阵法计算了模型的基本再生数R₀，利用Hurwitz判据和矩阵理论分析了平衡点的局部稳定性，这项研究聚焦于一种传染病动态模型，特点是综合考虑了环境病毒量和疫苗对传播的影响，得出了以下关键结论：1) 当基本再生数R₀小于1时，传染病无法持续传播，这是传染病控制的理想状态。2) 当R₀大于1时，为了有效地控制传染病传播，需要采取措施降低人们的接触率，并提高疫苗接种的覆盖率。这两个因素对传染病的传播有着重要而积极的影响。所以降低接触率以及提高疫苗接种效果能使得基本再生数R₀减小，即能够有效防治该类传染病。

Abstract: This paper investigates a class of SLEIRVW infectious disease dynamics models with the effects of environmental viral load and vaccines, provides in-depth dynamics analysis and calculations of the models, calculates the basic regeneration number R₀ of the models by the next-generation matrix method, and analyzes the local stability of the equilibrium points using Hurwitz’s criterion and matrix theory. This study focuses on an infectious disease dynamics model featuring the integrated consideration of the study focuses on the dynamics of an infectious disease, characterized by a combination of environmental viral load and vaccine effects on transmission, and draws the following key conclusions: 1) When the fundamental regeneration number, R₀, is less than 1, the infectious disease cannot be spread sustainably, which is the ideal state for infectious disease control. 2) When R₀ is greater than 1, effective control of the spread of the infectious disease requires measures to reduce the rate of exposure to the population and to increase the coverage of vaccinations. These two factors have an important and positive impact on the spread of infectious diseases. Therefore, reducing the contact rate and improving the effectiveness of vaccination can make the basic regeneration number R₀ decrease, that is, it can effectively control this type of infectious disease.