  In this paper we consider the fractional SIS 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
$\alpha \uparrow 1$ (the SIS model) is also given. We analyse the effects of
the fractional derivatives by comparing the SIS and the $\alpha$-SIS models.
