We propose a modification of the SLIAR (Susceptible- Latent-Symptomatic Infected- Asymptomatic- Recovered) mathematical-epidemiological model with vital dynamics. This model includes a vaccination control strategy, and a treatment to reduce the symptoms, also the symptomatic infected population is divided into two states according to its severity. The qualitative analysis shows the local stability of the disease-free equilibrium point and the endemic point. Simulations and the statistical sensitivity analysis are developed using a set of parameters for COVID-19, and we found that the transmission, recruitment, finally, vaccination rates are potential targets to control an outbreak.