This article analyzes the dynamic of an extended SEIR model for the spread of COVID-19 considering a system of 7 differential equations whose stages are susceptible, exposed, infected, quarantined, recovered, dead and vaccinated. The necessary and sufficient conditions are determined for non-negativity, delimitation, existence and uniqueness of the solution of the model, local stability of the equilibrium points and the next generation matrix method. The simulations made in Python complement the qualitative analysis of the mathematical model to conclude the behavior of the virus spread over time; the information shown in this work could also be useful for the development of new prevention measures.