Mathematical Modeling of Internet Gaming Disorder Dynamics with Behavioral Intervention, Using Physics-Informed Neural Networks (PINNs)

Abstract

Internet Gaming Disorder, formally recognised as a distinct condition in the World Health Organization’s eleventh revision of the International Classification of Diseases (ICD-11), has emerged as a growing behavioural-health concern, yet quantitative, dynamic frameworks for describing how such patterns emerge within a population and respond to behavioral intervention over time remain scarce relative to the extensive cross-sectional and clinical-assessment literature on the topic. In this work we develop and analyse an original compartmental mathematical model for the dynamics of Internet Gaming Disorder under active behavioral intervention. The model partitions a population into four interacting groups: susceptible individuals (S), individuals exhibiting Internet Gaming Disorder (G), individuals engaged in behavioral or clinical intervention (I), and recovered individuals who have re-established regulated gaming habits and exert a protective effect on their peers (R). The interactions among these groups are governed by a system of four coupled nonlinear ordinary differential equations. We establish the positivity and boundedness of solutions, identify a disorder-free equilibrium and a persistent-disorder equilibrium, and derive the basic reproduction number R0 using the Next Generation Matrix method. Local stability of both equilibria is analysed via the Jacobian matrix, characteristic polynomial, and Routh–Hurwitz criteria, showing that the disorder-free state is locally asymptotically stable whenever R0 < 1. To complement this analytical treatment, we implement a Physics-Informed Neural Network (PINN) that embeds the governing differential equations into its training objective, and use it to (i) solve the forward problem of reconstructing the population trajectories and (ii) solve the inverse problem of recovering unknown behavioural parameters directly from simulated observational data. The trained network reproduces the forward trajectories with normalized root-mean-square errors below 0.4, and recovers three of the four unknown parameters with relative error under 11%, while the weakly identifiable intervention-efficacy parameter is recovered with a larger, but bounded, error, a finding we discuss in terms of parameter identifiability. This hybrid analytical-computational framework offers a reproducible, quantitative basis for studying, and ultimately informing, behavioral and clinical intervention strategies aimed at Internet Gaming Disorder.