Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers
In this paper, we present a continuous mathematical model PMHTrTpQ of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number R0....
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2020-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2020/4903168 |
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| _version_ | 1850110815803277312 |
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| author | Bouchaib Khajji Abderrahim Labzai Omar Balatif Mostafa Rachik |
| author_facet | Bouchaib Khajji Abderrahim Labzai Omar Balatif Mostafa Rachik |
| author_sort | Bouchaib Khajji |
| collection | DOAJ |
| description | In this paper, we present a continuous mathematical model PMHTrTpQ of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number R0. We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number R0. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium E0 when R0≤1. When R0>1, drinking present equilibrium E∗ exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium E∗. |
| format | Article |
| id | doaj-art-4229dd0fc8be403e86d6acc0f3277ad9 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-4229dd0fc8be403e86d6acc0f3277ad92025-08-20T02:37:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252020-01-01202010.1155/2020/49031684903168Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment CentersBouchaib Khajji0Abderrahim Labzai1Omar Balatif2Mostafa Rachik3Laboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University Mohammedia, Sidi Othman, Casablanca, MoroccoLaboratory of Analysis Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’Sik, Hassan II University Mohammedia, 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 Mohammedia, Sidi Othman, Casablanca, MoroccoIn this paper, we present a continuous mathematical model PMHTrTpQ of alcohol drinking with the influence of private and public addiction treatment centers. We study the dynamical behavior of this model and we discuss the basic properties of the system and determine its basic reproduction number R0. We also study the sensitivity analysis of model parameters to know the parameters that have a high impact on the reproduction number R0. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at drinking-free equilibrium E0 when R0≤1. When R0>1, drinking present equilibrium E∗ exists and the system is locally as well as globally asymptotically stable at alcohol present equilibrium E∗.http://dx.doi.org/10.1155/2020/4903168 |
| spellingShingle | Bouchaib Khajji Abderrahim Labzai Omar Balatif Mostafa Rachik Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers International Journal of Mathematics and Mathematical Sciences |
| title | Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers |
| title_full | Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers |
| title_fullStr | Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers |
| title_full_unstemmed | Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers |
| title_short | Mathematical Modeling and Analysis of an Alcohol Drinking Model with the Influence of Alcohol Treatment Centers |
| title_sort | mathematical modeling and analysis of an alcohol drinking model with the influence of alcohol treatment centers |
| url | http://dx.doi.org/10.1155/2020/4903168 |
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