Fractional calculus has been widely used in mathematical modeling of evolutionary systems with memory effect on dynamics. The main interest of this work is, through a statistical approach, to attest how the hysteresis phenomenon, which describes the memory effect present in biological systems, can be treated by fractional calculus, and to analyze the contribution of the historical values of a function in the evaluation of fractional operators according their order. In order to illustrate the efficiency of this non-integer order calculus, we consider the SIR (Susceptible-Infected-Recovered) compartmental model which is widely used in epidemiology. We employ SIR models to model the dynamics, with and without memory, of the spread of Covid-19 in some countries.