  We study epidemic Susceptible-Infected-Susceptible models in the fractional
setting. The novelty is to consider models in which the susceptible and
infected populations evolve according to different fractional orders. We study
a model based on Caputo derivative, for which we establish existence results of
the solutions. Also, we investigate a model based on Caputo-Fabrizio operator,
for which we provide existence of solutions and a study of the equilibria.
Numerical simulations for both models and a direct numerical comparison are
also provided.
