Optimal Control of a Modified Mathematical Model of Social Media Addiction
Abstract
This research investigates the application of optimal control in the Susceptible, Exposed, Addicted, Recovery, Quit (SEA_1 A_2 RQ) model to address social media addiction. The primary objective is to develop an effective control strategy to reduce the prevalence of social media addiction. The methodology employs Pontryagin's maximum principle to formulate the optimal control problem, incorporating two time-dependent control variables: control (u_1) and treatment (u_2). The optimal control model is numerically simulated using the 4th-order Runge-Kutta method. Comparative analysis of the simulation results, with and without control, demonstrates significant differences in all population groups after four years. The findings reveal that implementing control (u_1) and treatment (u_2) markedly decreases the number of individuals addicted to social media, highlighting the efficacy of the proposed strategy in mitigating social media addiction.
Keywords: optimal control; social media addiction model; Pontryagin maximum principle.
Abstrak
Penelitian ini mengkaji penerapan kontrol optimal pada model Susceptible, Exposed, Addicted, Recovery, model Quit (SEA_1 A_2 RQ) untuk menangani kecanduan sosial media. Tujuan utama penelitian ini adalah untuk mengembangkan strategi kontrol yang efektif untuk mengurangi jumlah individu yang mengalami kecanduan media sosial. Metodologi penelitian ini menggunakan prinsip maksimum Pontryagin untuk merumuskan masalah kontrol optimal, yang menggabungkan dua variabel kontrol bergantung pada waktu: pengendalian (u_1) dan pengobatan (u_2). Model kontrol optimal disimulasikan secara numerik menggunakan metode Runge-Kutta orde 4. Analisis komparatif dari hasil simulasi, dengan dan tanpa kontrol, menunjukkan perbedaan yang signifikan pada semua kelompok populasi setelah empat tahun. Temuan tersebut mengungkapkan bahwa penerapan pengendalian (u_1) dan pengobatan (u_2) secara signifikan mengurangi populasi pengguna kecanduan sosial media, yang menyoroti kemanjuran strategi yang diusulkan untuk mengurangi kecanduan sosial media.
Kata Kunci: kontrol optimal; model kecanduan media sosial; prinsip maksimum Pontryagin.
2020MSC: 49N90, 91D10, 92B05.
Keywords
References
A. Rafiq, "Dampak Media Sosial Terhadap Perubahan Sosial Suatu Masyarakat," Statistik Pemuda Indonesia, vol. 18, pp. 18–29, 2020.
Badan Pusat Statistik, Statistik Pemuda Indonesia 2023, vol. 21, 2023.
A. P. Indah and D. A. Maulana, "Model Dinamika Kecanduan Media Sosial: Studi Kasus Kecanduan Social Media Pada Mahasiswa FMIPA UNESA," Jurnal Sains dan Teknologi, vol. 10, no. 1, pp. 131–139, 2022.
A. Anwar, R. Syam, M. I. Pratama, and S. Side, "SEIRS Model Analysis for Online Game Addiction Problem of Mathematics Students," Journal of Physics: Conference Series, vol. 1918, no. 4, pp. 1–10, 2021, doi: 10.1088/1742-6596/1918/4/042024.
S. Jamaludin, A. Syarifah, and Karyadi, "Faktor-Faktor Penyebab Kecanduan Media Sosial Pada Mahasiswa Fakultas Ilmu Kesehatan UIN Syarif Hidayatullah Jakarta," Jurnal Kesehatan, vol. 6, no. 2, 2022.
Kuswantoro, "Pendidikan Profetik untuk Anak di Era Digital: Upaya Menangani Kecanduan Gadget pada Anak," Jurnal Pendidikan, vol. 2, no. 1, pp. 87–99, 2020.
J. Wójcik-grudzień, M. Rozenbajgier, A. Ozga-stachurska, and P. Pawłowska, "Tourette Syndrom - a Review of Current Literature," Journal of Medical Sciences, vol. 12, no. 9, pp. 607–613, 2022.
C. Fremer et al., "Mass Social Media-Induced Illness Presenting With Tourette-Like Behavior," Journal of Movement Disorders, vol. 1, pp. 1–10, 2022.
H. T. Alemneh and N. Y. Alemu, "Mathematical Modeling with Optimal Control Analysis of Social Media Addiction," Infectious Disease Modelling, vol. 6, pp. 405–419, 2021, doi: 10.1016/j.idm.2021.01.011.
Z. A. Fikrina et al., "Analisis Dinamik Modifikasi Model Matematika Kecanduan Social Media," Jurnal Matematika dan Sains, 2024.
H. Huo and Q. Wang, "Modelling the Influence of Awareness Programs by Media on the Drinking Dynamics," Journal of Applied Mathematical Modelling, 2014.
T. Paulus et al., "Pandemic Tic-like Behaviors Following Social Media Consumption," Movement Disorders, vol. 36, no. 12, pp. 2932–2935, 2021, doi: 10.1002/mds.28800.
T. Li and Y. Guo, "Stability and Optimal Control in a Mathematical Model of Online Game Addiction," Journal of Game Addiction Studies, vol. 17, pp. 5691–5711, 2019.
A. E. Cavanna et al., "Dissecting the Gilles de la Tourette Spectrum: A Factor Analytic Study on 639 Patients," Journal of Neurology, Neurosurgery & Psychiatry, vol. 81, no. 3, pp. 1–10, 2011, doi: 10.1136/jnnp.2010.225029.
R. D. Freeman and C. Psychiatry, "An International Perspective on Tourette Syndrome: Selected Findings From 3500 Individuals in 22 Countries," International Journal of Psychiatry, vol. 10, no. 3, pp. 436–447, 2000.
DOI: 10.15408/inprime.v6i2.41438
Refbacks
- There are currently no refbacks.
.
