INVESTIGATING VIRUS SPREAD ANALYSIS IN COMPUTER NETWORKS WITH ATANGANA–BALEANU FRACTIONAL DERIVATIVE MODELS

Abstract

This paper proposes a mathematical model to investigate the dynamic behaviors of a modified computer virus model using the Atangana–Baleanu fractional derivative in the Caputo sense, aiming to elucidate the connection between its parameters and network attributes. By introducing a relatively new numerical method, we address the memory-dependent and nonlocal features of the system. The existence and uniqueness of the model’s solution are confirmed. To explore solution trajectories and assess the impact of various input factors on computer virus dynamics, we employ an efficient numerical technique. Our simulations provide insights into the consequences of fractional order, anti-virus measures, asymptotic fraction, damage rate, and removal rate in the system. These findings illuminate the relationships between model parameters, facilitating the design of networks that minimize the risk of virus outbreaks and prevent future cyber threats. By identifying critical factors involved in the progression of viruses, these results enable the development of more effective defense mechanisms.