Modeling and mathematical analysis of drug addiction with the study of the effect of psychological and biological treatment

: pp. 935–943
Received: November 17, 2022
Revised: June 17, 2023
Accepted: June 19, 2023

Mathematical Modeling and Computing, Vol. 10, No. 3, pp. 935–943 (2023)

Laboratory of Analysis, Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Science Ben M'sik, University of Hassan II, Casablanca, Morocco
Laboratory of Fundamental Mathematics and Their Applications, Department of Mathematics, Faculty of Sciences El Jadida, Chouaib Doukkali University, El Jadida, Morocco
Laboratory of Analysis, modeling and simulation, Department of mathematics and computer sciences, Faculty of sciences Ben M'Sik, University Hassan II of Casablanca

In this article, we propose a discrete mathematical model which describes the propagation of the drug phenomenon in a human population.  The population is unscrewed in five compartments: "$S$" People likely to become drug addicts, "$M$" Moderate drug addicts, "$H$" Heavy drug addicts, "$T$" People receiving drug addiction treatment, "$R$" The recovered people who have completely abstained from drug addiction.  Our goal is to find a better strategy to reduce the number of heavy addicts and to maximize the number of people receiving full treatment.  The tools of optimal control theory were used in this study, in particular the Pontryagin maximum principle.

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