  In this paper, we firstly propose SQIARD and SIARD models to investigate the
transmission of COVID-19 with quarantine, infected and asymptomatic infected,
and discuss the relation between the respective basic reproduction number $R_0,
R_Q$ and the stability of the equilibrium points of model. Secondly, after
training the related data parameters, in our numerical simulations, we
respectively conduct the forecast of the data of US, South Korea, Brazil,
India, Russia and Italy, and the effect of prediction of the epidemic situation
in each country. Furthermore, we apply US data to compare SQIARD with SIARD,
and display the effects of predictions.

Populations and Evolution;Physics and Society