Analysis of the COVID-19 model with self-protection and isolation measures affected by the environment

Since the global outbreak of COVID-19, the virus has continuously mutated and can survive in the air for long periods of time. This paper establishes and analyzes a model of COVID-19 with self-protection and quarantine measures affected by viruses in the environment to investigate the influence of viruses in the environment on the spread of the outbreak, as well as to develop a rational prevention and control measure to control the spread of the outbreak. The basic reproduction number was calculated and Lyapunov functions were constructed to discuss the stability of the model equilibrium points. The disease-free equilibrium point was proven to be globally asymptotically stable when $ R_0 < 1 $, and the endemic equilibrium point was globally asymptotically stable when $ R_0 > 1 $. The model was fitted using data from COVID-19 cases in Chongqing between November 1 to November 25, 2022. Based on the numerical analysis, the following conclusion was obtained: clearing the virus in the environment and strengthening the isolation measures for infected people can control the epidemic to a certain extent, but enhancing the self-protection of individuals can be more effective in reducing the risk of being infected and controlling the transmission of the epidemic, which is more conducive to the practical application.