The objectives of this study are to develop the $\mathtt{SEIR}$ model for Covid-19 and evaluate its main parameters such as therapeutic vaccines, vaccination rate and effectiveness of prophylactic. Global and local stability of the model and numerical simulation are examined. Local stability of equilibrium points was classified. A Lyapunov function is constructed to analyze global stability of the disease-free equilibrium. The simulation part is based on two situations, including the USA and Iran. Our results provide a good contribution to the current research on this topic.
