Modeling and Dynamical Analysis of Computer Worm Propagation using a New SEIR-Re Model and its Application with the Hausdorff Fractal Derivative

Computer worm is a type of malicious software that spreads through computer networks and it is a major threat to the security of the system since it can spread at a very high rate through one computer to another. This propagation may cause serious security vulnerability and therefore it is extremely crucial that the cybersecurity professionals are able to model the propagation of these threats. The conventional Susceptible, Exposed, Infected, Recovered model is improved by integrating reinfection states to generate a new mathematical model of worm propagation in this study. The appearance of this new class makes it possible to investigate in detail malware that has the ability to reinfect recovered nodes and discuss its more significant effects. In this paper, the equilibrium points of the proposed dynamic epidemic model are examined, and specifically calculating the basic reproduction number and assessing its effects on the equilibrium points. Moreover, the stability of such equilibrium points is also thoroughly studied. Hausdorff fractal derivative is then used to modify the proposed system. It is shown that the properties of the solutions are independent of various choices of derivatives, which means that Hausdorff fractal derivative can be used in a very broad set of circumstances. Furthermore, Runge-Kutta-Fehlberg method is used to conduct numerical simulations in order to validate the theoretical findings. The findings confirm that the given model is aligned with the requirements of the system and shows the application of the Hausdorff fractal derivative to be a strong and useful model of computer worm propagation.