Fractional SIS Epidemic Models

In this paper, we consider the fractional SIS (susceptible-infectious-susceptible) epidemic model (alpha-SIS model) in the case of constant population size. We provide a representation of the explicit solution to the fractional model and we illustrate the results by numerical schemes. A comparison with the limit case when the fractional order alpha converges to 1 (the SIS model) is also given. We analyze the effects of the fractional derivatives by comparing the SIS and the alpha-SIS models.