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

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dc.citation.epage943
dc.citation.issue3
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage935
dc.contributor.affiliationУніверситет Хасана ІІ Касабланки
dc.contributor.affiliationУніверситет Шуайба Дуккалі
dc.contributor.affiliationHassan II University of Casablanca
dc.contributor.affiliationChouaib Doukkali University
dc.contributor.authorМоуміне, Е. М.
dc.contributor.authorБалатіф, О.
dc.contributor.authorРачик, М.
dc.contributor.authorMoumine, E. M.
dc.contributor.authorBalatif, O.
dc.contributor.authorRachik, M.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T12:17:32Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractУ цій статті пропонується дискретна математична модель, яка описує поширення явища наркоманії серед людської популяції. Населення розділене на п’ять сегментів: “S” — люди, які можуть стати наркоманами, “M” — помірні наркомани, “H” — важкі наркомани, “T” — люди, які проходять лікування від наркозалежності, “R” — люди, які одужали та повністю утрималися від наркотичної залежності. Мета статті полягає в тому, щоб знайти кращу стратегію, щоб зменшити кількість важких наркозалежних і максимально збільшити кількість людей, які отримують повне лікування. У статті використовувався інструментарій теорії оптимального керування, зокрема принцип максимуму Понтрягіна.
dc.description.abstractIn 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.
dc.format.extent935-943
dc.format.pages9
dc.identifier.citationMoumine E. M. Modeling and mathematical analysis of drug addiction with the study of the effect of psychological and biological treatment / E. M. Moumine, O. Balatif, M. Rachik // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 3. — P. 935–943.
dc.identifier.citationenMoumine E. M. Modeling and mathematical analysis of drug addiction with the study of the effect of psychological and biological treatment / E. M. Moumine, O. Balatif, M. Rachik // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 3. — P. 935–943.
dc.identifier.doidoi.org/10.23939/mmc2023.03.935
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63530
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 3 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 3 (10), 2023
dc.relation.references[1] Khajji B., Boujallal L., Elhia M., Balatif O., Rachik M. A fractional-order model for drinking alcohol behaviour leading to road accidents and violence. Mathematical Modeling and Computing. 9 (3), 501–518(2022).
dc.relation.references[2] Sadki M., Harroudi S., Allali K. Dynamical analysis of an HCV model with cell-to-cell transmission and cure rate in the presence of adaptive immunity. Mathematical Modeling and Computing. 9 (3), 579–593 (2022).
dc.relation.references[3] Bounkaicha C., Allali K., Tabit Y., Danane J. Global dynamic of spatio-temporal fractional order SEIR model. Mathematical Modeling and Computing. 10 (2), 299–310 (2023).
dc.relation.references[4] Elkaf M., Allali K. Fractional derivative model for tumor cells and immune system competition. Mathematical Modeling and Computing. 10 (2), 288–298 (2023).
dc.relation.references[5] Hu Z., Teng Z., Jiang H. Stability analysis in a class of discrete SIRS epidemic model. Nonlinear Analysis: Real World Applications. 13 (5), 2017–2033 (2012).
dc.relation.references[6] Lenhart S., Workman J. T. Optimal control applied to biological models. Chapman and Hall/CRC, Boca Raton (2007).
dc.relation.references[7] Mushayabasa S., Tapedzesa G. Modeling illicit drug use dynamics and its optimal control analysis. Computational and Mathematical Methods in Medicine. 2015, 383154 (2015).
dc.relation.references[8] Rafal M. D., Stevens W. F. Discrete dynamic optimization applied to on-line optimal control. AlChE Journal. 14 (1), 85–91 (1968).
dc.relation.references[9] Martin R. B. Optimal control drug scheduling of cancer chemotherapy. Automatica. 28 (6), 1113–1123 (1992).
dc.relation.references[10] Mushayabasa S., Tapedzesa G. Modeling Illicit Drug Use Dynamics and Its Optimal Control Analysis. Computational and Mathematical Methods in Medicine. 2015, 383154 (2015).
dc.relation.references[11] Behrens D. A., Caulkins J. P., Tragler G., Feichtinger G. Optimal Control of Drug Epidemics: Prevent and Treat — But Not at the Same Time? Management Science. 46 (3), 333–347 (2000).
dc.relation.references[12] Khajji B., Moumine E. M, Ferjouchia H., Balatif O., Rachik M. Optimal control and discrete-time modelling of alcohol model with physical and psychological complications. Journal of Mathematical and Computational Science. 10 (5), 1969–1986 (2020).
dc.relation.references[13] Khajji B., Kouidere A., Balatif O., Rachik M. Mathematical modeling, analysis and optimal control of an alcohol drinking model with liver complication. Communications in Mathematical Biology and Neuroscience. 2020, 32 (2020).
dc.relation.references[14] Khajji B., Labzai A., Balatif O., Rachik M. Mathematical modeling and analysis of an alcohol drinking model with the influence of alcohol treatment centers. International Journal of Mathematics and Mathematical Sciences. 2020, 4903168 (2020).
dc.relation.references[15] Moore H. How to mathematically optimize drug regimens using optimal control. Journal of Pharmacokinetics and Pharmacodynamics. 45, 127–137 (2018).
dc.relation.references[16] Labzai A., Balatif O., Rachik M. Optimal control strategy for a discrete time smoking model with specific saturated incidence rate. Discrete Dynamics in Nature and Society. 2018, 5949303 (2018).
dc.relation.references[17] Njagarah J. B. H., Nyabadza F. Modelling the role of drug barons on the prevalence of drug epidemics. Mathematical Biosciences and Engineering. 10 (3), 843–860 (2013).
dc.relation.references[18] Labzai A., Kouidere A., Khajji B., Balatif O., Rachik M. Mathematical Modeling and Optimal Control Strategy for a Discrete Time Drug Consumption Model. Discrete Dynamics in Nature and Society. 2020, 5671493 (2020).
dc.relation.references[19] Khajji B., Labzai A., Kouidere A., Balatif O., Rachik M. A discrete mathematical modeling of the influence of alcohol treatment centers on the drinking dynamics using optimal control. Journal of Applied Mathematics. 2020, 9284698 (2020).
dc.relation.references[20] Athans M., Falb P. L. Optimal Control: An Introduction tothe Theory and Its Applications. Dover Publications (2006).
dc.relation.references[21] Liberzon D. Calculus of Variations and Optimal Control Theory. A Concise Introduction. Princeton University Press, Princeton, NJ, USA (2012).
dc.relation.references[22] Chinchuluun A., Pardalos P. M., Enkhbat R., Tseveendori I. (Eds.) Optimization and Optimal Control: Theory and Applications. Vol. 39. Springer (2010).
dc.relation.references[23] Stengel R. F. Optimal Control and Estimation. Dover, New York, USA (1994).
dc.relation.references[24] Chen P., Islam S. M. N. Optimal Control Models in Finance: A New Computation Approach. Springer (2005).
dc.relation.references[25] Ani¸ta S., Arn˘autu V., Capasso V. An Introduction to Optimal Control Problems in Life Sciences and Economics: From Mathematical Models to Numerical Simulation with MATLAB. Birkh¨auser (2011).
dc.relation.references[26] La Torre D., Kunze H., Ruiz-Galan M., Malik T., Marsiglio S. Optimal control: theory and application to science,engineering, and social sciences. 2015, 890527 (2015).
dc.relation.references[27] Ding W., Hendon R., Cathey B., Lancaster E., Germick R. Discrete time optimal control applied to pest control problems. Involve, A Journal of Mathematics. 7 (4), 479–489 (2014).
dc.relation.references[28] Guibout V., Bloch A. M. A discrete maximum principle for solving optimal control problems. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). 1806–1811 (2004).
dc.relation.references[29] Hwang C. L., Fan L. T. A discrete version of Pontryagin’s maximum principle. Operations Research. 15 (1), 139–146 (1967).
dc.relation.references[30] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F. The Mathematical Theory of Optimal Processes. John Wiley & Sons, London (1962).
dc.relation.referencesen[1] Khajji B., Boujallal L., Elhia M., Balatif O., Rachik M. A fractional-order model for drinking alcohol behaviour leading to road accidents and violence. Mathematical Modeling and Computing. 9 (3), 501–518(2022).
dc.relation.referencesen[2] Sadki M., Harroudi S., Allali K. Dynamical analysis of an HCV model with cell-to-cell transmission and cure rate in the presence of adaptive immunity. Mathematical Modeling and Computing. 9 (3), 579–593 (2022).
dc.relation.referencesen[3] Bounkaicha C., Allali K., Tabit Y., Danane J. Global dynamic of spatio-temporal fractional order SEIR model. Mathematical Modeling and Computing. 10 (2), 299–310 (2023).
dc.relation.referencesen[4] Elkaf M., Allali K. Fractional derivative model for tumor cells and immune system competition. Mathematical Modeling and Computing. 10 (2), 288–298 (2023).
dc.relation.referencesen[5] Hu Z., Teng Z., Jiang H. Stability analysis in a class of discrete SIRS epidemic model. Nonlinear Analysis: Real World Applications. 13 (5), 2017–2033 (2012).
dc.relation.referencesen[6] Lenhart S., Workman J. T. Optimal control applied to biological models. Chapman and Hall/CRC, Boca Raton (2007).
dc.relation.referencesen[7] Mushayabasa S., Tapedzesa G. Modeling illicit drug use dynamics and its optimal control analysis. Computational and Mathematical Methods in Medicine. 2015, 383154 (2015).
dc.relation.referencesen[8] Rafal M. D., Stevens W. F. Discrete dynamic optimization applied to on-line optimal control. AlChE Journal. 14 (1), 85–91 (1968).
dc.relation.referencesen[9] Martin R. B. Optimal control drug scheduling of cancer chemotherapy. Automatica. 28 (6), 1113–1123 (1992).
dc.relation.referencesen[10] Mushayabasa S., Tapedzesa G. Modeling Illicit Drug Use Dynamics and Its Optimal Control Analysis. Computational and Mathematical Methods in Medicine. 2015, 383154 (2015).
dc.relation.referencesen[11] Behrens D. A., Caulkins J. P., Tragler G., Feichtinger G. Optimal Control of Drug Epidemics: Prevent and Treat - But Not at the Same Time? Management Science. 46 (3), 333–347 (2000).
dc.relation.referencesen[12] Khajji B., Moumine E. M, Ferjouchia H., Balatif O., Rachik M. Optimal control and discrete-time modelling of alcohol model with physical and psychological complications. Journal of Mathematical and Computational Science. 10 (5), 1969–1986 (2020).
dc.relation.referencesen[13] Khajji B., Kouidere A., Balatif O., Rachik M. Mathematical modeling, analysis and optimal control of an alcohol drinking model with liver complication. Communications in Mathematical Biology and Neuroscience. 2020, 32 (2020).
dc.relation.referencesen[14] Khajji B., Labzai A., Balatif O., Rachik M. Mathematical modeling and analysis of an alcohol drinking model with the influence of alcohol treatment centers. International Journal of Mathematics and Mathematical Sciences. 2020, 4903168 (2020).
dc.relation.referencesen[15] Moore H. How to mathematically optimize drug regimens using optimal control. Journal of Pharmacokinetics and Pharmacodynamics. 45, 127–137 (2018).
dc.relation.referencesen[16] Labzai A., Balatif O., Rachik M. Optimal control strategy for a discrete time smoking model with specific saturated incidence rate. Discrete Dynamics in Nature and Society. 2018, 5949303 (2018).
dc.relation.referencesen[17] Njagarah J. B. H., Nyabadza F. Modelling the role of drug barons on the prevalence of drug epidemics. Mathematical Biosciences and Engineering. 10 (3), 843–860 (2013).
dc.relation.referencesen[18] Labzai A., Kouidere A., Khajji B., Balatif O., Rachik M. Mathematical Modeling and Optimal Control Strategy for a Discrete Time Drug Consumption Model. Discrete Dynamics in Nature and Society. 2020, 5671493 (2020).
dc.relation.referencesen[19] Khajji B., Labzai A., Kouidere A., Balatif O., Rachik M. A discrete mathematical modeling of the influence of alcohol treatment centers on the drinking dynamics using optimal control. Journal of Applied Mathematics. 2020, 9284698 (2020).
dc.relation.referencesen[20] Athans M., Falb P. L. Optimal Control: An Introduction tothe Theory and Its Applications. Dover Publications (2006).
dc.relation.referencesen[21] Liberzon D. Calculus of Variations and Optimal Control Theory. A Concise Introduction. Princeton University Press, Princeton, NJ, USA (2012).
dc.relation.referencesen[22] Chinchuluun A., Pardalos P. M., Enkhbat R., Tseveendori I. (Eds.) Optimization and Optimal Control: Theory and Applications. Vol. 39. Springer (2010).
dc.relation.referencesen[23] Stengel R. F. Optimal Control and Estimation. Dover, New York, USA (1994).
dc.relation.referencesen[24] Chen P., Islam S. M. N. Optimal Control Models in Finance: A New Computation Approach. Springer (2005).
dc.relation.referencesen[25] Ani¸ta S., Arn˘autu V., Capasso V. An Introduction to Optimal Control Problems in Life Sciences and Economics: From Mathematical Models to Numerical Simulation with MATLAB. Birkh¨auser (2011).
dc.relation.referencesen[26] La Torre D., Kunze H., Ruiz-Galan M., Malik T., Marsiglio S. Optimal control: theory and application to science,engineering, and social sciences. 2015, 890527 (2015).
dc.relation.referencesen[27] Ding W., Hendon R., Cathey B., Lancaster E., Germick R. Discrete time optimal control applied to pest control problems. Involve, A Journal of Mathematics. 7 (4), 479–489 (2014).
dc.relation.referencesen[28] Guibout V., Bloch A. M. A discrete maximum principle for solving optimal control problems. 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601). 1806–1811 (2004).
dc.relation.referencesen[29] Hwang C. L., Fan L. T. A discrete version of Pontryagin’s maximum principle. Operations Research. 15 (1), 139–146 (1967).
dc.relation.referencesen[30] Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mishchenko E. F. The Mathematical Theory of Optimal Processes. John Wiley & Sons, London (1962).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectоптимальне керування
dc.subjectматематична модель
dc.subjectдискретна модель
dc.subjectнаркотична залежність
dc.subjectoptimal control
dc.subjectmathematical model
dc.subjectdiscrete model
dc.subjectdrug addiction
dc.titleModeling and mathematical analysis of drug addiction with the study of the effect of psychological and biological treatment
dc.title.alternativeМоделювання та математичний аналіз наркоманії з вивченням ефекту психологічного та біологічного лікування
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 3