Analysis of COVID-19 Community Transmission and Prevention in the Post-Pandemic Era Based on Saturation Incidence Rates

本文研究了一类总人口为常数的具有饱和发生率和饱和移出率的SIRS传染病模型，得到了模型的基本再生数，分析了无病平衡点的局部渐近稳定和不稳定的条件，同时获得了地方病平衡点的存在唯一性条件以及渐近稳定性条件。进一步通过数值模拟对相关因素进行分析，为社区应对传染病提供建议。In this paper, the authors studied a class of SIRS infectious disease models with a constant total population, saturation incidence and saturation removal rates, obtained the basic reproduction number of the model, analyzed the conditions for local asymptotic stability and instability of disease-free equilibrium points, and obtained the conditions for the existence, uniqueness, and asymptotic stability of endemic equilibrium points. Furthermore, numerical simulations were conducted to analyze relevant factors and provide recommendations for community response to infectious diseases.