Dynamics of COVID-19 models with asymptomatic infections and quarantine measures

Considering the propagation characteristics of COVID-19 in different regions, the dynamics analysis and numerical demonstration of long-term and short-term models of COVID-19 are carried out, respectively. The long-term model is devoted to investigate the global stability of COVID-19 model with asymptomatic infections and quarantine measures. By using the limit system of the model and Lyapunov function method, it is shown that the COVID-19-free equilibrium $V^0$ is globally asymptotically stable if the control reproduction number $\mathcal{R}_{c}<1$ and globally attractive if $\mathcal{R}_{c}=1$, which means that COVID-19 will die out; the COVID-19 equilibrium $V^{\ast}$ is globally asymptotically stable if $\mathcal{R}_{c}>1$, which means that COVID-19 will be persistent. In particular, to obtain the local stability of $V^{\ast}$, we use proof by contradiction and the properties of complex modulus with some novel details, and we prove the weak persistence of the system to obtain the global attractivity of $V^{\ast}$. Moreover, the final size of the corresponding short-term model is calculated and the stability of its multiple equilibria is analyzed. Numerical simulations of COVID-19 cases show that quarantine measures and asymptomatic infections have a non-negligible impact on the transmission of COVID-19.