Mathematical Model Dynamics of Cyber Accounts for Vices, Recovery and Relapse
Year: 2025
Author: Oluwatayo Michael Ogunmiloro, Samuel Olukayode Ayinde
Journal of Nonlinear Modeling and Analysis, Vol. 7 (2025), Iss. 1 : pp. 91–110
Abstract
In this study, we develop a mathematical model through a system of first-order nonlinear ordinary differential equations. This model covers the dynamics between vulnerable cyber accounts and those implicated in cyber vices such as bullying, scams, spreading of misinformation, and the creation of harmful digital footprints. It further explores the mechanisms of recovery and relapse among these accounts. Through some mathematical analysis, we apply relevant theorems to affirm the model’s fundamental properties, which includes its existence, uniqueness, positivity, and boundedness. We also determine the model’s cyber vice-free and endemic equilibrium states, analyzing their local and global asymptotic stability based on when the basic reproduction number Rcb is greater or less than one. Simulation exercises are conducted to substantiate our theoretical findings and demonstrate the model’s behavior in relation to Rcb. The simulation outcomes reveal an escalating trend in cyber vices, showing the necessity for targeted interventions that promote a more secure online environment for users and the broader cyber space.
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2025.91
Journal of Nonlinear Modeling and Analysis, Vol. 7 (2025), Iss. 1 : pp. 91–110
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Local stability global stability positivity and boundedness basic reproduction number Rcb.
Author Details
Oluwatayo Michael Ogunmiloro Email
Samuel Olukayode Ayinde Email