Modeling Fractional-Differential Dynamics of Computer Virus Propagation Based on a Diffusive Epidemiological Model

This paper considers a two-dimensional, non-local-in-time diffusive mathematical model of the epidemiological dynamics of computer viruses, which generalizes the SIES model. The model system with Caputo derivatives of piecewise-constant order consists of equations for three unknown functions, two of which are expressed in closed form as solutions to the corresponding linear boundary value problems. A qualitative analysis of the nonlinear boundary value problem with respect to the third unknown function, representing the number of infected nodes, is performed. A numerical solution method and some results of computer modeling of the fractional-order virus propagation dynamics in a network are presented.