Abstract: To investigate the dynamics of COVID-19 infectious disease with environmental virus effects, we establish an SEIARc model and analyse its dynamic behaviors. Firstly, the next generation matrix method is used to calculate the basic reproduction number R^*₀. When R^*₀ <1, the disease-free equilibrium exists and is locally asymptotically stable. Furthermore, by using of Metzler matrix and other related theories, we prove that the globally asymptotic stability of the disease-free equilibrium. When R^*₀>1, the system always has a unique endemic equilibrium, and the conditions for the locally asymptotic stability of the equilibrium of endemic diseases are given. Finally, by numerical simulation, the results of the theoretical analysis and the globally asymptotic stability of the endemic equilibrium is verified. It is shown that the transmission of COVID-19 disease can be effectively controlled by reducing the source of the environmental virus or cutting off the transmission routes.

Key words: COVID-19, environmental virus, SEIARc model, basic reproduction number, stability