Abstract
Stochastic and fractional differentiation have been developed independently to depicting processes following randomness and power, a declining memory and passage from one process to another respectively. Very recently, fractional stochastic differential equations were suggested with the aim to capture processes following at the same time randomness and memory nonlocality. In this paper to further explore the applicability of this type of differential equations, a SIR model was considered and analyzed analytically and numerically. Some numerical simulations are presented for different values of fractional orders and densities of randomness.