A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control
Joint Authors
Rachik, Mostafa
Kouidere, Abdelfatah
Balatif, Omar
Labzai, Abderrahim
Khajji, Bouchaib
Source
Journal of Applied Mathematics
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-02-19
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Khajji, Bouchaib& Labzai, Abderrahim& Kouidere, Abdelfatah& Balatif, Omar& Rachik, Mostafa. 2020. A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control. Journal of Applied Mathematics،Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1174606
Modern Language Association (MLA)
Khajji, Bouchaib…[et al.]. A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control. Journal of Applied Mathematics No. 2020 (2020), pp.1-13.
https://search.emarefa.net/detail/BIM-1174606
American Medical Association (AMA)
Khajji, Bouchaib& Labzai, Abderrahim& Kouidere, Abdelfatah& Balatif, Omar& Rachik, Mostafa. A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control. Journal of Applied Mathematics. 2020. Vol. 2020, no. 2020, pp.1-13.
https://search.emarefa.net/detail/BIM-1174606
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1174606