A MATHEMATICAL MODEL SEABRQ WITH OPTIMAL CONTROL FOR SOCIAL MEDIA ADDICTION INCORPORATING COGNITIVE DYSREGULATION

Authors

DOI:

https://doi.org/10.25077/jmua.15.3.388-405.2026

Keywords:

compartmental model, optimal control, social media addiction

Abstract

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.

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Published

31-07-2026

Issue

Vol. 15 No. 3 (2026)

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