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  3. Volume 10, Number 1, 2023
  4. Mathematical modeling of the gaming disorder model with media coverage: optimal control approach

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

MMC.
2023;
Volume 10, Number 1
: pp. 245–260
https://doi.org/10.23939/mmc2023.01.245
Received: July 20, 2022
Revised: January 11, 2023
Accepted: January 15, 2023

Mathematical Modeling and Computing, Vol. 10, No. 1, pp. 245–260 (2023)

Authors:
  1. D. Kada
  2. A. Kouidere
  3. O. Balatif
  4. M. Rachik
1
Laboratory of Information Technology and Modeling, Department of Mathematics and Computer Science, Faculty of Sciences Ben M'Sick, Hassan II University of Casablanca, Morocco
2
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
3
Laboratory of Dynamical Systems, Mathematical Engineering Team (INMA), Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco
4
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.

 

gaming disorder
mathematical model
media coverage
optimal control
local stability
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