A MATHEMATICAL MODEL SEABRQ WITH OPTIMAL CONTROL FOR SOCIAL MEDIA ADDICTION INCORPORATING COGNITIVE DYSREGULATION - EVA SALSABILA; Yudi Ari Adi (Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang, 2026)
This study proposes a SEABRQ compartmental model to analyze social media addiction transmission and its cognitive consequences, referred to as cognitive dysregulation or 'brain rot.' The total population is partitioned into six compartments: Susceptible (S), Engaged (E), Addicted (A), Cognitively Dysregulated (B), Regulated (R), and Quit (Q). R_0 is computed using the next-generation matrix approach, and local asymptotic stability of both equilibrium points is established analytically. Sensitivity analysis identifies transmission rate and contact rate as the parameters most strongly amplifying R_0. An optimal control framework is incorporated into the model with two time-dependent control variables: u_1(t), representing preventive and early regulation interventions targeting susceptible and engaged populations, and u_2(t), representing treatment and behavioral support directed at addicted and cognitively dysregulated individuals. The optimal control problem is solved by applying Pontryagin’s Maximum Principle. Numerical simulations using the fourth-order Runge-Kutta method demonstrate that the combined application of both controls produces the most significant reduction in social media addiction persistence and its cognitive dysregulation effects over a five-year horizon.