Mathematical modeling of the gaming disorder model with media coverage: optimal control approach

: pp. 245–260
Received: July 20, 2022
Revised: January 11, 2023
Accepted: January 15, 2023
Laboratory of Information Technology and Modeling, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, Morocco
Laboratory of Analysis, Modeling, and Simulation (LAMS), Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, Morocco
Laboratory of Dynamical Systems, Mathematical Engineering Team (INMA), Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco
Laboratory of Analysis, Modeling and Simulation, Casablanca, Morocco

In this article, we propose a PEARM mathematical model to depict the dynamic of a population that reacts in the spread of the gaming disorder with media coverage.  The basic reproduction number and existence of free equilibrium point and endimec equilibrium point are obtained with same fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated.  By using Routh–Hurwitz criteria, the local stability of free equilibrium point and endimec equilibrium point are obtained.  Also, we propose an optimal strategy to implement the optimal campaigns through directing children and adolescents to educational and entertaining alternative means, and creating centers to restore the rehabilitation of addicts to electronic games.  The existence of the optimal control are obtained by Pontryagain's maximum principle.  Finally, some numerical simulations are also performed to illustrate the theoretical analysis of our results, using Matlab software.  Our results show that media coverage is an effective measure to quit electronic gaming disorder.


  1. Gentile D. A.  Pathological Video-Game Use Among Youth Ages 8 to 18: A National Study.  Psychological Science.  20 (5), 594–602 (2009).
  2. Bender P. K., Gentile D. A.  Internet gaming disorder: Relations between needs satisfaction in-game and in life in general.  Psychology of Popular Media.  9 (2), 266–278 (2019).
  3. American Psychiatric Association.  Diagnostic and Statistical Manual of Mental Disorders. Arlington, VA (2013).
  4. Sharpening the focus on gaming disorder.  Bulletin of the World Health Organization.  97, 382–383 (2019).
  5. Funk J. B., Hagan J., Schimming J., Bullock W. A., Buchman D. D., Myers M.  Aggression and psychopathology in adolescents with a preference for violent electronic games.  Aggressive Behavior.  28 (2), 134–144 (2002).
  6. Huesmann L. R.  The Impact of Electronic Media Violence: Scientific Theory and Research.  Journal of Adolescent Health.  41 (6), S6–S13 (2007).
  7. Baranowski T., Frankel L.  Let's Get Technical! Gaming and Technology for Weight Control and Health Promotion in Children.  Childhood Obesity.  8 (1), 34–37 (2012).
  8. Straker L., Abbott R., Collins R., Campbell A.  Evidence-based guidelines for wise use of electronic games by children.  Ergonomics.  57 (4), 471–489 (2014).
  9. Duven E. C., Müller K. W., Beutel M. E., Wölfling K.  Altered reward processing in pathological computer gamers – ERP-results from a semi-natural Gaming–Design.  Brain and Behavior.  5 (1), e00293 (2015).
  10. Etindele Sosso F. A., Kuss D. J., Vandelanotte C., Jasso-Medrano J. L. et al.  Insomnia, sleepiness, anxiety and depression among different types of gamers in African countries.  Scientific Reports. 10, 1937 (2020).
  11. Sadki M., Harroudi S., Allali K.  Dynamical analysis of an HCV model with cell-to-cell transmission and cure rate in the presence of adaptive immunity.  Mathematical Modeling and Computing.  9 (3), 579–593 (2022).
  12. Khajji B., Boujallal L., Elhia M., Balatif O., Rachik M.  A fractional-order model for drinking alcohol behaviour leading to road accidents and violence.  Mathematical Modeling and Computing.  9 (3), 501–518 (2022).
  13. Khaloufi I., Lafif M., Benfatah Y., Laarabi H., Bouyaghroumni J., Rachik M.  A continuous SIR mathematical model of the spread of infectious illnesses that takes human immunity into account.  Mathematical Modeling and Computing.  10 (1), 53–65 (2023).
  14. El Youssoufi L., Kouidere A., Kada D., Balatif O., Daouia A., Rachik M.  On stability analysis study and strategies for optimal control of a mathematical model of hepatitis HCV with the latent state.  Mathematical Modeling and Computing.  10 (1), 101–118 (2023).
  15. Kada D., Khajji B., Balatif O., Rachik M., Labriji E. H.  Optimal Control Approach of Discrete Mathematical Modeling of the Spread of Gaming Disorder in Morocco and Cost-Effectiveness Analysis.  Discrete Dynamics in Nature and Society.  2021, 5584315 (2021).
  16. Guo Y., Li T.  Optimal control strategies for an online game addiction model with low and high risk exposure.  Discrete and Continuous Dynamical Systems – B.  26 (10), 5355–5382 (2021).
  17. Kada D., Labriji A., Balatif O., Rachik M., Labriji H.  Mathematical modeling and stability analysis of endemic equilibrium point of gaming disorder.  Journal of Mathematical and Computational Science.  11 (5), 6279–6295 (2021).
  18. Wang Z., Petrosian O.  On class of non transferable utility cooperative differential games with continuous updating.  Journal of Dynamics and Games.  7 (4), 291–302 (2020).
  19. Kuss D. J., Griffiths M. D., Pontes H. M.  Chaos and confusion in DSM-5 diagnosis of Internet Gaming Disorder: Issues, concerns, and recommendations for clarity in the field.  Journal of Behavioral Addictions.  6 (2), 103–109 (2017).
  20. Rokkum J. N., Blanco–Herrera J. A., Faulhaber M. E., Gentile D. A.  Internet Gaming Disorder.  In: Moreno M., Radovic A. (eds) Technology and Adolescent Mental Health. Springer, Cham (2018).
  21. Rokkum J. N., Gentile D. A.  Primary Versus Secondary Disorder in the Context of Internet Gaming Disorder.  Current Addiction Reports.  5, 485–490 (2018).
  22. Krahé B., Möller I.  Playing violent electronic games, hostile attributional style, and aggression-related norms in German adolescents.  Journal of Adolescence.  27 (1), 53–69 (2004).
  23. Lemmens J. S., Hendriks S. J. F.  Addictive Online Games: Examining the Relationship Between Game Genres and Internet Gaming Disorder.  Cyberpsychology, Behavior and Social Networking.  19 (4), 270–276 (2016).
  24. Funk J. B., Buchman D. D., Germann J. N.  Preference for violent electronic games, self-concept and gender differences in young children.  American journal of Orlhopsychiaty.  70 (2), 233–241 (2000).
  25. Huo H.-F., Huang S.-R., Wang X.-Y., Xiang H.  Optimal control of a social epidemic model with media coverage.  Journal of Biological Dynamics.  11 (1), 226–243 (2017).
  26. Samanta S., Rana S., Sharma A., Misra A. K., Chattopadhyay J.  Effect of awareness programs by media on the epidemic outbreaks: A mathematical model.  Applied Mathematics and Computation.  219 (12), 6965–6977 (2013).
  27. Liu Y., Cui J.-A.  The impact of media converage on the dynamics of infectious diseases.  International Journal of Biomathematics.  1 (1), 65–74 (2008).
  28. Wang Y., Cao J. D., Jin Z., Zhang H. F., Sun G.-Q.  Impact of media coverage on epidemic spreading in complex networks.  Physica A: Statistical Mechanics and its Applications.  392 (23), 5824–5835 (2013).
  29. Bani-Yaghoub M., Gautam R., Shuai Z., Van den Driessche P., Ivanek R.  Reproduction numbers for infections with free-living pathogens growing in the environment.  Journal of Biological Dynamics.  6 (2), 923–940 (2012).
  30. Van den Driessche P., Watmough J.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission.  Mathematical Biosciences.  180 (1–2), 29–48 (2002).
  31. Kot M.  Elements of Mathematical Biology.  Cambridge University Press, Cambridge (2001).
  32. Fleming W. H., Rishel R. W.  Deterministic and Stochastic Optimal Control. Springer, New York, NY, USA (1975).
  33. Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F.  The Mathematical Theory of Optimal Processes. Wiley, New York, NY, USA (1962).
Mathematical Modeling and Computing, Vol. 10, No. 1, pp. 245–260 (2023)

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