Mathematical modeling with optimal control analysis of the spread and persistence of PUBG mobile addiction

PUBG Mobile addiction has become a growing global public health concern, particularly among adolescents and young adults, due to its highly fascinating gameplay and widespread accessibility through mobile devices. Excessive engagement with PUBG Mobile has been linked to serious psychological, behavioral, and social consequences, including anxiety, depression, sleep disorders, academic decline, and impaired interpersonal relationships. The rapid increase in problematic gaming behavior highlights the urgent need for scientifically grounded strategies to understand, predict, and effectively control the spread of PUBG Mobile addiction at the population level. In this study, we created a deterministic mathematical model of PUBG Mobile addiction (PMA) and an optimal control model for it. Qualitative analysis was analyzed, including the basic reproduction number, the addiction-free equilibrium point, and the addicted persistence equilibrium point. The PUBG Mobile addiction-free equilibrium point (PMAFE) is locally asymptotically stable if. The Castillo-Chavez theorem is used to establish the global asymptotic stability of PMAFE. If, the unique addicted persistence equilibrium points is asymptotically stable locally. The model exhibits a forward bifurcation using the Center Manifold theorem at. The sensitivity analysis is performed to determine the most sensitive parameters. In the numerical simulation of the PMA model, the NSFD scheme is implemented, and the addicted and treated populations gradually decrease, stabilize, and drop over time, demonstrating the model’s accuracy. We also created an optimal control model, added two time-dependent controls to the original model, and applied Pontryagin’s maximum principle to perform optimal control analysis. The efficiency analysis is performed to investigate the optimal control strategy. The numerical simulations of the suggested optimal control PMA model approach utilize the fourth-order Runge-Kutta forward-backward sweep method. Finally, we conclude that stakeholders and policymakers must use the integrated control strategy C to control the PUBG Mobile addiction population worldwide.