Optimal control strategies for taming TikTok addiction: a mathematical model and analysis

Abstract Optimal control theory is an extension of the calculus of variations. It is a mathematical optimization method for deriving control strategies for a dynamic system. In this paper, the system of differential equations for which we aim to utilize control theory is TikTok, which is one of the most attractive internet platforms. TikTok has garnered immense popularity, surpassing other social media platforms. However, its addictive nature has raised concerns about mental health, including depression, eating disorders, anxiety, self-obsession, and narcissistic personality disorder among its users. This paper introduces a mathematical model for TikTok, considering the usage of this app as an epidemic. The model is rigorously validated through stability analysis of both local and global equilibrium. Moreover, disease-free and non-trivial equilibrium scenarios are discussed by calculating their reproduction numbers. This study aims to raise awareness of TikTok’s potential misuse and explore control theory solutions to mitigate addiction. Additionally, statistical data is used to visualize the numerical results and analyze the impact of control parameters on the TikTok model.