In this paper, COVID-19 virus model with effect the carrier to outbreak of epidemic is investigated. The outbreak of Covid-19 virus, is described by a mathematical model divided the population into four classes. The first class describes the susceptible unaware to disease, the second class the susceptible with has aware to disease by media coverage, the third class the carrier individuals and the last class is infected individuals. The existence, uniqueness and bounded-ness of the solutions of the model are discussed. All possible equilibrium points are determined. The locally asymptotically stable of the model is studied. Suitable Lyapunov functions are used to investigate the globally asymptotical stability of the model. Finally, numerical simulation is carried out to confirm the analytical results and understand the effect of varying the parameters on spread of disease.