A Mathematical Model with Time Delay for Addressing Online Game Addiction Through Family Time Intervention Based on Local Wisdom in South Sulawesi

Source abstract

This study analyzes the dynamics of online game addiction among FMIPA UNM students using a modified time-delayed SEAFR (Susceptible–Exposed–Addicted–Family time–Recovered) mathematical model. Online game addiction is a growing concern that threatens academic performance and social well-being. The research applies a five-stage methodology: (1) literature review of SIR-based models and digital addiction studies to identify compartments and parameters; (2) data collection from 400 students through proportionate stratified random sampling; (3) model development incorporating time delay, cultural norms, and family-based interventions; (4) equilibrium and stability analysis using Jacobian matrices and Routh–Hurwitz criteria; and (5) numerical simulations with MATLAB to evaluate intervention strategies. The analysis yields a basic reproduction number, R₀ = 0.5, indicating that addictive behavior tends to decline without reinforcement of exposure. However, the endemic equilibrium remains locally asymptotically stable, suggesting addiction may persist if interventions are weak. Simulation results highlight that reducing exposure (β), enhancing recovery through awareness and cultural support (γ), and strengthening family-based activities significantly reduce addiction prevalence. These findings show the usefulness of mathematical modeling as a decision-support tool contextualized by local wisdom, offering practical insights for policymakers and educators in designing effective interventions to address student addiction.