Dynamical Analysis of Modified Mathematical Model of Social Media Addiction

Juhari Juhari, Zulfa Akfi Fikrina, Evawati Alisah, Imam Sujarwo

Abstract


In this study, there is no division between addiction in the mild and severe stages. Therefore, it is necessary to divide the stages of addiction because the healing is clearly different. Therefore, in this study, a modified dynamic analysis of the Social Media addiction model is carried out to obtain a valid model that can be implemented in real life. This study aims to find the stability of changes in the Addicted variable which is divided into two, namely Social Media addiction in the mild stage and Social Media addiction in the severe stage  There are six models that have been modified in this study, namely, individuals who do not have Social Media but are vulnerable to addiction , individuals who have Social Media but are not yet at the addiction stage , individuals infected with Social Media addiction in the mild stage , individuals infected with Social Media addiction in the severe stage , individuals who are recovering from Social Media addiction , individuals who are completely recovered from Social Media addiction . The steps of dynamic analysis include determining the equilibrium point, analyzing the stability of the equilibrium point, finding the basic reproduction number, numerical simulation of all variables. The results showed that the population of individuals infected with Social Media addiction in the mild stage  was at a value of 1.6112 with t = 4 years while the population of individuals infected with Social Media addiction in the severe stage  was at a value of 36.542 with t = 4 years. This study provides information that the dynamic analysis carried out on the modified mathematical model of Social Media addiction shows a stable condition.


Keywords


Dynamic Analysis; Model Modification; Social Media Addiction Model

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References


[1] Li, T., & Guo, Y. (2019). Stability and optimal control in a mathematical model of online game addiction. Filomat, 33(17), 5691–5711. https://doi.org/10.2298/FIL1917691L

[2] Hartinah, S., Sriati, A., & Kosasih, C. E. (2019). Gambaran Tingkat Gejala Kecanduan Media Sosial pada Mahasiswa Keperawatan Universitas Padjadjaran. VII(1), 123–133. https://doi.org/10.31311/JK.V7I1.4769

[3] Kermack, W., & McKendrick, A. (1927). Contributions To The Mathematical Theory Of Epidemics. Bulletin of Mathematical Biology. https://doi.org/10.1016/S0092-8240(05)80040-0

[4] Abi, M. M., Bano, E. N., Obe, L. F., & Blegur, F. M. A. (2023). Pemodelan Matematika dan Simulasi Kecanduan Media Sosial Social Media Tipe SEI1I2R. 5(1), 43–55. http://dx.doi.org/10.35508/jd.v5i1.10401

[5] Syam, R., Side, S., & Said, C. S. (2021). Model SEIRS Penyebaran Penyakit Tuberkulosis di Kota Makassar. Journal of Mathematics Computations and Statistics, 3(1), 11. https://doi.org/10.35580/jmathcos.v3i1.19180

[6] Qin, Y., Omar, B., & Musetti, A. (2022). The addiction behavior of short-form video app Social Media: The information quality and system quality perspective. Frontiers in Psychology, 13(September). https://doi.org/10.3389/fpsyg.2022.932805

[7] Gill, C. E., & Kompoliti, K. (2019). Clinical Features of Tourette Syndrome. https://doi.org/10.1177/0883073819877335

[8] Anurogo, D. (2014). Fenomenologi Sindrom Tourette. Cdk-211, 40(12), 900–906. https://www.researchgate.net/publication/261166739_Fenomenologi_Sindrom_Tourette

[9] Aprilia, R., Sriati, A., & Hendrawati, S. (2018). Tingkat Kecanduan Media Sosial pada Remaja. 3(1), 41–53. http://dx.doi.org/10.24198/jnc.v3i1.26928

[10] Al Addawiyah, A. F., & Fuad, Y. (2023). Model Dinamik SEARQ dan Penerapan Kontrol Optimal pada Permasalahan Kecanduan Media Sosial. MATHunesa: Jurnal Ilmiah Matematika, 11(1), 67–81. https://doi.org/10.26740/mathunesa.v11n1.p67-81

[11] Indah, A. P., & Maulana, D. A. (2022). Model Dinamika Kecanduan Media Sosial : Studi Kasus Kecanduan Social Media pada Mahasiswa FMIPA UNESA. https://doi.org/10.26740/mathunesa.v10n1.p131-139

[12] Sugiyono. (2012). Buku Metode Penelitian Sugiyono. Data Kualitatif, p. 12. https://scholar.google.com/citations?user=MGOs5rkAAAAJ

[13] Dettman, J. W., Boyce, W. E., & DiPrima, R. C. (1967). Elementary Differential Equations and Boundary Value Problems. In The American Mathematical Monthly (Vol. 74). https://doi.org/10.2307/2314317

[14] Alemneh, H. T., & Alemu, N. Y. (2021). Mathematical modeling with optimal control analysis of social media addiction. Infectious Disease Modelling, 6, 405–419. https://doi.org/10.1016/j.idm.2021.01.011

[15] Iswanto, R. J. (2012). Pemodelan Matematika Aplikasi dan Terapannya. Yogyakarta: Graha Ilmu. https://www.semanticscholar.org/paper/Pemodelan-Matematika-%3A-Aplikasi-dan-Terapannya-Iswanto/452500df5265b8ab2d54f9d9392d38a2fa04fa7a

[16] Yeung, A., Ng, E., & Abi-Jaoude, E. (2022). Social Media and Attention-Deficit/Hyperactivity Disorder: A Cross-Sectional Study of Social Media Content Quality. Canadian Journal of Psychiatry, 67(12), 899–906. https://doi.org/10.1177/07067437221082854

[17] Laili, F. M., & Nuryono, W. (2015). Penerapan Konseling Keluarga Untuk Mengurangi Kecanduan Game Online Pada Siswa Kelas Vii Smp Negeri 21 Surabaya. Itnow, 50(4). https://doi.org/10.1093/itnow/bwn071

[18] Fremer, C., Szejko, N., Pisarenko, A., Haas, M., Laudenbach, L., Wegener, C., & Müller-Vahl, K. R. (2022). Mass social media-induced illness presenting with Tourette-like behavior. Frontiers in Psychiatry, 13(1). https://doi.org/10.3389/fpsyt.2022.963769

[19] Matonya, F. L., & Kuznetsov, D. (2021). Mathematical Modelling of Drug Abuse and it’s Effect in the Society. Annals of Pure and Applied Mathematics, 24(02), 159–176. https://doi.org/10.22457/apam.v24n2a06855

[20]Estévez, A., Jáuregui, P., Sánchez-Marcos, I., López-González, H., & Griffiths, M. D. (2017). Attachment and emotion regulation in substance addictions and behavioral addictions. Journal of Behavioral Addictions, 6(4), 534–544. https://doi.org/10.1556/2006.6.2017.086

[21] Momani, S., Chauhan, R. P., Kumar, S., & Hadid, S. (2023). Analysis of Social Media Addiction Model With Singular Operator. Fractals, (March). https://doi.org/10.1142/S0218348X23400972

[22] Zea Vera, A., Bruce, A., Garris, J., Tochen, L., Bhatia, P., Lehman, R. K., … Gilbert, D. L. (2022). The Phenomenology of Tics and Tic-Like Behavior in Social Media. Pediatric Neurology, 130, 14–20. https://doi.org/10.1016/j.pediatrneurol.2022.02.003

[23] Guo, Y., & Li, T. (2020). Optimal control and stability analysis of an online game addiction model with two stages. Mathematical Methods in the Applied Sciences, 43(7), 4391–4408. https://doi.org/10.1002/mma.6200

[24] Huo, H. F., & Wang, Q. (2014). Modelling the influence of awareness programs by media on the drinking dynamics. Abstract and Applied Analysis, 2014. https://doi.org/10.1155/2014/938080

[25] Griffiths, M. D. (2001). Griffiths, M.D. (2001). Excessive internet use: Implications for education. Education and Health, 19, 23-29. Retrieved from https://www.academia.edu/429636/Griffiths_M_D_2001_Excessive_internet_use_Implications_for_education_Education_and_Health_19_23_29

[26] Wang, X. Y., Huo, H. F., Kong, Q. K., & Shi, W. X. (2014). Optimal control strategies in an alcoholism model. Abstract and Applied Analysis, 2014. https://doi.org/10.1155/2014/954069

[27] Diekmann, & Heesterbeek, J. (2000). Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation - O. Diekmann, J. A. P. Heesterbeek. Wiley Series, 322. Retrieved from http://eu.wiley.com/WileyCDA/WileyTitle/productCd-0471492418.html

[28] Hasnawati, H., Ratianingsih, R., & Puspita, J. W. (2017). Analisis Kestabilan Model Matematika Pada Penyebaran Kanker Serviks Menggunakan Kriteria Routh-Hurwitz. Jurnal Ilmiah Matematika Dan Terapan, 14(1), 120–127. https://doi.org/10.22487/2540766x.2017.v14.i1.8360

[29] Sofiah. (2013). Analisa Penentuan Harga Gain Untuk Kestabilan Pada Sistem Pengendali Dengan Metode Routh-Hurwitz. Berkala Teknik, 3(2), 530–542. https://jurnal.um-palembang.ac.id/berkalateknik/article/view/358

[30] Giesecke, J. (2017a). Modern infectious disease epidemiology: Third edition. Modern Infectious Disease Epidemiology: Third Edition, 1–233. https://doi.org/10.1201/9781315222714




DOI: https://doi.org/10.18860/ca.v9i2.29225

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