Before revision:  We examine the explicit representation and the numerical schemes for the limit case of the fractional order \alpha  , corresponding to the well-known ordinary SIS model, and we analyse the effects of the fractional derivatives by comparing the two models.
After revision:  We examine the explicit representation and the numerical schemes for the limit case of the fractional order \alpha  \uparrow 1 (the SIS model) is also given. We analyse the effects of the fractional derivatives by comparing the two models.