A Fractional Computer Virus Propagation Model with Saturation Effect

The epidemic modeling of computer virus propagation is identified as an effective approach to understanding the mechanism of virus spread. Fraction-order virus spread models exhibit remarkable advantages over their integer-order counterparts. Based on a type of bursting virus, a fractional computer virus propagation model with saturation effect is suggested. The basic properties of the model are discussed. The basic reproduction number of the model is determined. The virus–endemic equilibria of the model are determined. A criterion for the global asymptotic stability of the virus-free equilibrium is derived. For a pair of potential virus–endemic equilibria, criteria for the local asymptotic stability are presented. Some interesting properties of the model, ranging from the impact of the fractional order and the saturation index on virus spread to their coupling effect, are revealed through numerical simulations. This work helps gain a deep insight into the laws governing virus propagation.