A Fractional Calculus Model for Worm Propagation in Computer Network

Fractional Calculus emerges as a new field with wide applications in the fields of science and engineering. There is an increasing trend to find fractional calculus applications in various real-life nonlinear and non-local problems, to develop new models for existing problems. Various results reported by the researchers, and many more are on the way to be discovered. Among all these problems is a computer science problem, worm propagation over various networks. This paper will provide an overview of existing worm propagation models and their applications in analyzing and combating computer virus threats using fractional calculus. We specifically look at various classical and fractional models described in the literature for mobile and computer networks. This work makes an important addition by developing a fractional SEIR model that uses the Caputo derivative to represent worm spread in a network context. This model's equilibrium points and asymptotic stability are systematically examined to better understand its dynamical behavior.This paper aims to present some short summaries of the work by distinguished researchers in modeling virus and worm propagation problems using fractional calculus. We believe this incomplete, but important, information will guide many researchers and help them to see some of the main real-world applications and gain an understanding of this powerful mathematical tool. We expect this collection will also benefit our community. Along with this a fractional SEIR model of virus propagation with the help of Caputo derivative is taken in this work. Its equilibrium point and asymptotic stability are discussed.