Eva Salsabila, Yudi Ari Adi
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.