Periodic solutions and coexistence states in a competitive system of two serotypes with superinfection

In this paper we tackled out a model to study the phenomena of superinfection, that is we consider two serotypes I 1 and I 2 of the same type of disease acting on the same population, a competitive system. Assuming that the total population is fixed, we reduce the model to a bidimensional systems of ODE. In the first part we consider that all coefficients in the equations are constant. Then we describe the coexistence state and its stability in terms of the Reproduction Number corresponding to both serotypes. In the second part, we introduce periodic coefficients in the same model, and analyze the corresponding model with periodic coefficients, which now is a non-autonomous system. We give the necessary and sufficient conditions to have periodic orbits and non trivial coexistence states, in the last case we also show the conditions to have local stability of them. In both cases we do several numerical simulations to illustrate some of the phenomena that we are describing.