The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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APPLYING THE PUARL MATHEMATICAL MODEL: PSYCHOLOGICAL INSIGHTS FOR RESTRICTING GAMING AND INTERNET ADDICTION

  • Mohit Soni (Department of Mathematics, Government Holkar (Model, Autonomous) Science College) ;
  • Rajesh Kumar Sharma (Department of Mathematics, J.N.S. Government PG College) ;
  • Shivram Sharma (Government Postgraduate College)
  • Received : 2024.02.04
  • Accepted : 2024.08.15
  • Published : 2024.11.30
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Abstract

Consider social media and gaming addiction as diseases and consider their harmful effects on the user's health. This research introduces a PUARL epidemic model to prevent their spread among the population through psychological awareness. It calculates the basic reproduction number, analyzes stability, and conducts a sensitivity analysis. The study emphasizes the importance of psychological factors in preventing addiction, highlighting the role of psychological awareness.

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References

  1. Alemneh, H.T. & Alemu, N.Y.: Mathematical modeling with optimal control analysis of social media addiction. Infectious Disease Modelling 6 (2021), 405-419. https://doi.org/10.1016/j.idm.2021.01.011 
  2. Balakrishnan, J. & Griffiths, M.D.: Social media addiction: What is the role of content in YouTube?. Journal of behavioral addictions 6 (2017), no. 3, 364-377. https://doi.org/10.1556/2006.6.2017.058 
  3. Blower, S.M. & Dowlatabadi, H.: Sensitivity and uncertainty analysis of complex models of disease transmission: an HIV model, as an example. International Statistical Review/Revue Internationale de Statistique, 229-243. https://doi.org/10.2307/1403510 
  4. https://www.bloomberg.com/news/articles/2022-02-23/video-game-addiction-recognized-by-world-health-organization accessed on 2 January 2024. 
  5. https://www.bhaskar.com/who-told-mobile-game-addiction-in-the-category-of-disorder-kept-brain-disease-5902462.html/ accessed on 2 January 2024. 
  6. Castillo-Chavez, C. & Song, B.: Dynamical models of tuberculosis and their applications. Math. Biosci. Eng. 1 (2004), no. 2, 361-404. https://doi.org/10.3934/mbe.2004.1.361 
  7. Castillo-Chavez, C., Blower, S., van den Driessche, P., Kirschner, D. & Yakubu, A.A.(Eds.): Mathematical approaches for emerging and reemerging infectious diseases: models, methods, and theory (Vol. 126). Springer Science & Business Media, 2002. https://doi.org/10.1007/978-1-4613-0065-6 
  8. Chakraborty, K., Basu, D., & Kumar, K.V.: Internet addiction: Consensus, controversies, and the way ahead. East Asian Archives of Psychiatry 20 (2010), no. 3, 123-132. https://search.informit.org/doi/10.3316/informit.935942388038735 
  9. Cheng, C., Lau, Y.C., Chan, L. & Luk, J.W.: Prevalence of social media addiction across 32 nations: Meta-analysis with subgroup analysis of classification schemes and cultural values. Addictive behaviors 117 (2021), 106845. https://doi.org/10.1016/j.addbeh.2021.106845 
  10. Darvesh, N., Radhakrishnan, A., Lachance, C.C., Nincic, V., Sharpe, J.P., Ghassemi, M., ... & Tricco, A.C.: Exploring the prevalence of gaming disorder and Internet gaming disorder: A rapid scoping review. Systematic reviews 9 (2020), 1-10. https://doi.org/10.1186/s13643-020-01329-2 
  11. Edition, F.: Diagnostic and statistical manual of mental disorders. Am Psychiatric Assoc. 21 (2013), no. 21, 591-643. https://doi.org/10.1176/appi.books.9780890425596 
  12. Gentile, D.A., Bailey, K., Bavelier, D., Brockmyer, J.F., Cash, H., Coyne, S.M., ... & Young, K.: Internet gaming disorder in children and adolescents. Pediatrics 140(Supplement 2) (2017), S81-S85. https://doi.org/10.1542/peds.2016-1758H 
  13. Guedes, E., Nardi, A.E., Guimaraes, F. M.C.L., Machado, S. & King, A.L.S.: Social networking, a new online addiction: a review of Facebook and other addiction disorders. Medical Express 3 (2016), M160101. https://doi.org/10.5935/MedicalExpress.2016.01.01 
  14. Guo, Y. & Li, T.: Optimal control and stability analysis of an online game addiction model with two stages. Mathematical Methods in the Applied Sciences 43 (2020), no. 7, 4391-4408. https://doi.org/10.1002/mma.6200 
  15. Guo, Y. & Li, T.: Fractional-order modeling and optimal control of a new online game addiction model based on real data. Communications in Nonlinear Science and Numerical Simulation 121 (2023), 107221. https://doi.org/10.1016/j.cnsns.2023.107221 
  16. Hou, Y., Xiong, D., Jiang, T., Song, L. & Wang, Q.: Social media addiction: Its impact, mediation, and intervention. Cyberpsychology 13 (2019), no. 1. https://doi.org/10.5817/CP2019-1-4 
  17. Ishaku, A., Musa, B.S., Sanda, A. & Bakoji, A.M.: Mathematical assessment of social media impact on academic performance of students in higher institution. IOSR J. Math. 2018 (2018), 72-79. https://doi.org/10.9790/5728-1401017279 
  18. Kermack, W.O. & McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proceedings of the royal society of london. Series A, Containing papers of a mathematical and physical character 115 (1927), no. 772, 700-721. https://doi.org/10.1098/rspa.1927.0118 
  19. Khajji, B., Labzai, A., Balatif, O. & Rachik, M.: Mathematical modeling and analysis of an alcohol drinking model with the influence of alcohol treatment centers. International Journal of Mathematics and Mathematical Sciences 2020 (2020), 1-12. https://doi.org/10.1155/2020/4903168 
  20. Kim, H.S., Son, G., Roh, E.B., Ahn, W.Y., Kim, J., Shin, S.H., ... & Choi, K.H.: Prevalence of gaming disorder: A meta-analysis. Addictive behaviors 126 (2022), 107183. https://doi.org/10.1016/j.addbeh.2021.107183 
  21. King, D.L. & Delfabbro, P.H.: The cognitive psychology of Internet gaming disorder. Clinical psychology review 34 (2014), no. 4, 298-308. https://doi.org/10.1016/j.cpr.2014.03.006. 
  22. Ko, C.H.: Internet gaming disorder. Current Addiction Reports 1 (2014), 177-185. https://doi.org/10.1007/s40429-014-0030-y 
  23. Kolan, B.J. & Dzandza, P.E.: Effect of social media on academic performance of students in Ghanaian Universities: A case study of University of Ghana, Legon. Library Philosophy and Practice (2018), 0 1-24. https://core.ac.uk/download/pdf/189476898.pdf 
  24. LaSalle, J.P.: The stability of dynamical systems, society for industrial and applied mathematics, Philadelphia, pa., 1976. In With an appendix:"Limiting equations and stability of nonautonomous ordinary differential equations" by Z. Artstein, Regional Conference Series in Applied Mathematics (1976). https://doi.org/10.1137/1.9781611970432 
  25. Lemmens, J.S., Valkenburg, P M. & Gentile, D.A.: The internet gaming disorder scale. Psychological assessment 27 (2015), no. 2, 567. https://doi.org/10.1037/pas0000062 
  26. Li, T., & Guo, Y.: Stability and optimal control in a mathematical model of online game addiction. Filomat 33 (2019), no. 17, 5691-5711. https://doi.org/10.2298/FIL1917691L 
  27. Ma, S.H., Huo, H.F., & Meng, X.Y.: Modelling alcoholism as a contagious disease: a mathematical model with awareness programs and time delay. Discrete Dynamics in Nature and Society 2015 (2015). https://doi.org/10.1155/2015/260195 
  28. Malak, M.Z., Shuhaiber, A.H., Al-amer, R.M., Abuadas, M.H. & Aburoomi, R.J.: Correlation between psychological factors, academic performance and social media addiction: model-based testing. Behaviour & Information Technology 41 (2022), no. 8, 1583-1595. https://doi.org/10.1080/0144929X.2021.1891460 
  29. Mills, D.J. & Allen, J.J.: Self-determination theory, internet gaming disorder, and the mediating role of self-control. Computers in Human Behavior 105 (2020), 106209. https://doi.org/10.1016/j.chb.2019.106209 
  30. Monacis, L., De Palo, V., Griffiths, M.D. & Sinatra, M.: Social networking addiction, attachment style, and validation of the Italian version of the Bergen Social Media Addiction Scale. Journal of behavioral addictions6 (2017), no. 2, 178-186. https://doi.org/10.1556/2006.6.2017.023 
  31. Murray, J.D.: Mathematical biology: I. An introduction. Interdisciplinary applied mathematics. Mathematical Biology, Springer, 17, 2002. https://doi.org/10.1007/b98868 
  32. Petry, N.M., Rehbein, F., Gentile, D.A., Lemmens, J.S., Rumpf, H.J., Mossle, T., ... & O'Brien, C.P.: An international consensus for assessing internet gaming disorder using the new DSM-5 approach. Addiction 109 (2014), no. 9, 1399-1406. https://doi.org/10.1111/add.12457 
  33. Petry, N.M., Rehbein, F., Ko, C.-H. & O'Brien, C.P.: (2015). Internet gaming disorder in the DSM-5. Current Psychiatry Reports 17 (2015), no. 9, 72. https://doi.org/10.1007/s11920-015-0610-0 
  34. Pontes, H.M. & Griffiths, M.D.: Measuring DSM-5 internet gaming disorder: Development and validation of a short psychometric scale. Computers in Human Behavior 45 (2015), 137-143. https://doi.org/10.1016/j.chb.2014.12.006 
  35. Przybylski, A.K., Weinstein, N. & Murayama, K.: Internet gaming disorder: Investigating the clinical relevance of a new phenomenon. American Journal of Psychiatry 174 (2017), no. 3, 230-236. https://doi.org/10.1176/appi.ajp.2016.16020224 
  36. Saunders, J.B., Hao, W., Long, J., King, D.L., Mann, K., Fauth-Buhler, M. ... & Poznyak, V.: Gaming disorder: Its delineation as an important condition for diagnosis, management, and prevention. Journal of behavioral addictions 6 (2017), no. 3, 271-279. https://doi.org/10.1556/2006.6.2017.039 
  37. Sharma, S., Soni, M. & Sharma, D.R.K.: 'Unveiling the Psychological Consequences of Social Media Addiction: A PUARL Model Approach'. Available at SSRN 4625112. https://dx.doi.org/10.2139/ssrn.4625112 
  38. Shek, D.T., Tang, V.M. & Lo, C.Y.: Internet addiction in Chinese adolescents in Hong Kong: assessment, profiles, and psychosocial correlates. The Scientific World Journal 8 (2008), 776-787. https://doi.org/10.1100/tsw.2008.104 
  39. Sharma, S. & Sharma, P.K.: A study of SIQR model with Holling type-II incidence rate. Malaya Journal of Matematik 9 (2021), no. 01, 305-311. https://doi.org/10.26637/MJM0901/0052 
  40. Siddiqui, S. & Singh, T.: Social media its impact with positive and negative aspects. International journal of computer applications technology and research 5 (2016), no. 2, 71-75. http://dx.doi.org/10.7753/IJCATR0502.1006 
  41. Simsek, A., Elciyar, K. & Kizilhan, T.: A comparative study on social media addiction of high school and university students. Contemporary educational technology 10 (2019), no. 2, 106-119. https://doi.org/10.30935/cet.554452 
  42. Soni, M., Sharma, R.K. & Sharma, S.: The basic reproduction number and herd immunity for COVID-19 in India. Indian Journal of Science and Technology 14 (2021), no. 35, 2773-2777. https://doi.org/10.17485/IJST/v14i35.797 
  43. Stevens, M.W., Dorstyn, D., Delfabbro, P.H. & King, D.L.: Global prevalence of gaming disorder: A systematic review and meta-analysis. Australian & New Zealand Journal of Psychiatry. 55 (2021), no. 6, 553-568. https://doi.org/10.1177/0004867420962851 
  44. Sujarwoto, Saputri, R.A.M. & Yumarni, T.: Social media addiction and mental health among university students during the COVID-19 pandemic in Indonesia. International journal of mental health and addiction 21 (2023), no. 1, 96-110. https://doi.org/10.1177/0004867420962851 
  45. Van den Driessche, P. & Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Mathematical biosciences 180 (2002), no. 1-2, 29-48. https://doi.org/10.1016/S0025-5564(02)00108-6 
  46. Wang, X.Y., Huo, H.F., Kong, Q.K. & Shi, W.X.: Optimal control strategies in an alcoholism model. In Abstract and Applied Analysis 2014 (2014, January), Hindawi. https://doi.org/10.1155/2014/954069 
  47. https://www.who.int/standards/classifications/frequently-asked-questions/gaming-disorder accessed 2 january 2024. 
  48. Wong, H.Y., Mo, H.Y., Potenza, M.N., Chan, M.N.M., Lau, W.M., Chui, T.K. ... & Lin, C.Y.: Relationships between severity of internet gaming disorder, severity of problematic social media use, sleep quality and psychological distress. International journal of environmental research and public health 17, no. 6, 1879. https://doi.org/10.3390/ijerph17061879 
  49. Zajac, K., Ginley, M.K. & Chang, R.: Treatments of internet gaming disorder: a systematic review of the evidence. Expert review of neurotherapeutics 20, no. 1, 85-93. https://doi.org/10.1080/14737175.2020.1671824