In the Staged Progression (SP) epidemic models, infected individuals are
classified into a suitable number of states. The goal of these models is to
describe as closely as possible the effect of differences in infectiousness
exhibited by individuals going through the different stages. The main objective
of this work is to study, from the methodological point of view, the behavior
of solutions of the discrete time SP models without reinfection and with a
general incidence function. Besides calculating R0​, we find
bounds for the epidemic final size, characterize the asymptotic behavior of the
infected classes, give results about the final monotonicity of the infected
classes, and obtain results regarding the initial dynamics of the prevalence of
the disease. Moreover, we incorporate into the model the probability
distribution of the number of contacts in order to make the model amenable to
study its effect in the dynamics of the disease