  We propose a compartmental model for a disease with temporary immunity and
secondary infections. From our assumptions on the parameters involved in the
model, the system naturally evolves in three time scales. We characterize the
equilibria of the system and analyze their stability. We find conditions for
the existence of two endemic equilibria, for some cases in which $\mathcal{R}_0
< 1$. Then, we unravel the interplay of the three time scales, providing
conditions to foresee whether the system evolves in all three scales, or only
in the fast and the intermediate ones. We conclude with numerical simulations
and bifurcation analysis, to complement our analytical results.
