Mathematical Model Dynamics of Cyber Accounts for Vices, Recovery and Relapse (Journal of Nonlinear Modeling and Analysis, 2025)
In this study, we develop a mathematical model through a systemof first-order nonlinear ordinary differential equations. This model covers thedynamics between vulnerable cyber accounts and those implicated in cybervices such as bullying, scams, spreading of misinformation, and the creation ofharmful digital footprints. It further explores the mechanisms of recovery andrelapse among these accounts. Through some mathematical analysis, we applyrelevant theorems to affirm the model’s fundamental properties, which includesits existence, uniqueness, positivity, and boundedness. We also determinethe model’s cyber vice-free and endemic equilibrium states, analyzing theirlocal and global asymptotic stability based on when the basic reproductionnumber $R_{cb}$ is greater or less than one. Simulation exercises are conducted tosubstantiate our theoretical findings and demonstrate the model’s behavior inrelation to $R_{cb}.$ The simulation outcomes reveal an escalating trend in cybervices, showing the necessity for targeted interventions that promote a moresecure online environment for users and the broader cyber space.
Keywords: Local stability; global stability; positivity and boundedness; basic reproduction number $R_{cb}.$