A general model for the spread of contagious diseases is proposed. It takes into account susceptible, isolated, exposed, asymptomatic and symptomatic infected, hospitalized, deceased and recovered persons. The social interaction and some other aspects, as the psychological reaction of the population when the number of infected people increases, are incorporated in a nonlinear incidence rate. The existence and stability of the equilibria is analyzed and the reproduction number is computed. Various types of bifurcations are analyzed and the results are interpreted from the epidemiological point of view. The theoretical study is completed by numerical simulations.