A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control
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...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2020/9284698 |
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| author | Bouchaib Khajji Abderrahim Labzai Abdelfatah Kouidere Omar Balatif Mostafa Rachik |
| author_facet | Bouchaib Khajji Abderrahim Labzai Abdelfatah Kouidere Omar Balatif Mostafa Rachik |
| author_sort | Bouchaib Khajji |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2036c391722e4302a7b046e2e9cea417 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2036c391722e4302a7b046e2e9cea4172025-02-03T06:43:26ZengWileyJournal of Applied Mathematics1110-757X1687-00422020-01-01202010.1155/2020/92846989284698A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal ControlBouchaib Khajji0Abderrahim Labzai1Abdelfatah Kouidere2Omar Balatif3Mostafa Rachik4Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University, Sidi Othman, Casablanca, MoroccoLaboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University, Sidi Othman, Casablanca, MoroccoLaboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University, Sidi Othman, Casablanca, MoroccoMathematical Engineering Team (INMA), Laboratory of Dynamical Systems, Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, MoroccoLaboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University, Sidi Othman, Casablanca, MoroccoIn 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.http://dx.doi.org/10.1155/2020/9284698 |
| spellingShingle | Bouchaib Khajji Abderrahim Labzai Abdelfatah Kouidere Omar Balatif Mostafa Rachik A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control Journal of Applied Mathematics |
| title | A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control |
| title_full | A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control |
| title_fullStr | A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control |
| title_full_unstemmed | A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control |
| title_short | A Discrete Mathematical Modeling of the Influence of Alcohol Treatment Centers on the Drinking Dynamics Using Optimal Control |
| title_sort | discrete mathematical modeling of the influence of alcohol treatment centers on the drinking dynamics using optimal control |
| url | http://dx.doi.org/10.1155/2020/9284698 |
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