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A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control

Author

Listed:
  • Bouchaib Khajji
  • Abderrahim Labzai
  • Abdelfatah Kouidere
  • Omar Balatif
  • Mostafa Rachik

Abstract

In this paper, we propose a discrete mathematical model that describes the interaction between the classes of drinkers, namely, potential drinkers (P), moderate drinkers (M), heavy drinkers (H), poor heavy drinkers (Tp), rich heavy drinkers (Tr), and quitters of drinking (Q). We also focus on the importance of treatment within addiction treatment centers aiming to find the optimal strategies to minimize the number of drinkers and maximize the number of heavy drinkers who join addiction treatment centers. We use three controls which represent awareness programs through media and education for the potential drinkers, efforts to encourage the heavy drinkers to join addiction treatment centers, and psychological support with follow‐up for the individuals who quit drinking. We use Pontryagin’s maximum principle in discrete time to characterize these optimal controls. The resulting optimality system is solved numerically by Matlab. Consequently, the obtained results confirm the performance of the optimization strategy.

Suggested Citation

  • Bouchaib Khajji & Abderrahim Labzai & Abdelfatah Kouidere & Omar Balatif & Mostafa Rachik, 2020. "A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    • Handle: RePEc:wly:jnljam:v:2020:y:2020:i:1:n:9284698
    DOI: 10.1155/2020/9284698
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    References listed on IDEAS

    as
    1. Hai-Feng Huo & Qian Wang, 2014. "Modelling the Influence of Awareness Programs by Media on the Drinking Dynamics," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Xun-Yang Wang & Hai-Feng Huo & Qing-Kai Kong & Wei-Xuan Shi, 2014. "Optimal Control Strategies in an Alcoholism Model," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. Hai-Feng Huo & Qian Wang, 2014. "Modelling the Influence of Awareness Programs by Media on the Drinking Dynamics," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, April.
    4. C. L. Hwang & L. T. Fan, 1967. "A Discrete Version of Pontryagin's Maximum Principle," Operations Research, INFORMS, vol. 15(1), pages 139-146, February.
    5. Xun-Yang Wang & Hai-Feng Huo & Qing-Kai Kong & Wei-Xuan Shi, 2014. "Optimal Control Strategies in an Alcoholism Model," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-18, March.
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    Cited by:

    1. Abdelfatah Kouidere & Abderrahim Labzai & Hanane Ferjouchia & Omar Balatif & Mostafa Rachik, 2020. "A New Mathematical Modeling with Optimal Control Strategy for the Dynamics of Population of Diabetics and Its Complications with Effect of Behavioral Factors," Journal of Applied Mathematics, John Wiley & Sons, vol. 2020(1).
    2. Lemesa Bedjisa Dano & Koya Purnachandra Rao & Temesgen Duressa Keno, 2022. "Modeling the Combined Effect of Hepatitis B Infection and Heavy Alcohol Consumption on the Progression Dynamics of Liver Cirrhosis," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).

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