Analysis of global stability of an epidemic model with asymptomatic infected persons

Asymptomatic infection is an important feature that distinguishes COVID-19 from known SARS viral diseases. In this paper, we propose a new mathematical model for virus transmission with asymptomatic infected persons, which can be used for COVID-19. We study the model by defining the basic reproduction number ( $R_{0}$ ), showing the nonnegativity and boundedness of the solution, and constructing proper Lyapunov function, the global stability of the disease-free equilibrium and the endemic equilibrium are obtained. Numerical simulation of the model shows that the threshold of the basic reproduction number can determine the global asymptotic stability of the equilibria. Moreover, by simulating and analyzing the model, we obtain that the number of people diagnosed for COVID-19 will increase, and the number of hospital beds should be increased to meet the large number of patients with the implementation of the screening strategy. Therefore, to control the spread of the epidemic, increase in the detection of asymptomatic infected persons is very important.