Optimal Control Approach of Discrete Mathematical Modeling of the Spread of Gaming Disorder in Morocco and Cost-Effectiveness Analysis

Abstract

We highlight and study in this paper the phenomenon of the spread of addiction to electronic games, where the addict goes through stages before reaching the degree of addiction. In order to model this phenomenon, we have divided people into four groups, which are potential gamers, engaged gamers, addicted gamers, and gamers who have recovered from addiction. We propose a discrete mathematical model with control strategies using three controls that represent, respectively, $u_k$ , which represents awareness of the dangers of electronic games through written and visual media; $v_k$ , which represents the effort to direct children and adolescents to educational and entertaining alternative means; and $w_k$ , which represents creating rehabilitation centers for addicts to quit electronic game addiction. To characterize optimal controls, we use Pontryagin’s maximum principle and the system of optimality solved by an iterative method. Finally, numerical simulations are presented with and without controls. Using a cost-effectiveness analysis, we will show that the control that represents the creation of rehabilitation centers for gaming addicts is the most cost-effective strategy to control the spread of gaming addiction.