Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays
In this paper, we formulate an optimal control problem based on a tuberculosis model with multiple infectious compartments and time delays. In order to have a more realistic model that allows highlighting the role of detection, loss to follow-up and treatment in TB transmission, we propose an extens...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Balikesir University
2021-01-01
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| Series: | An International Journal of Optimization and Control: Theories & Applications |
| Subjects: | |
| Online Access: | http://www.ijocta.org/index.php/files/article/view/885 |
| _version_ | 1797913493798649856 |
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| author | Mohamed Elhia Omar Balatif Lahoucine Boujallal Mostafa Rachik |
| author_facet | Mohamed Elhia Omar Balatif Lahoucine Boujallal Mostafa Rachik |
| author_sort | Mohamed Elhia |
| collection | DOAJ |
| description | In this paper, we formulate an optimal control problem based on a tuberculosis model with multiple infectious compartments and time delays. In order to have a more realistic model that allows highlighting the role of detection, loss to follow-up and treatment in TB transmission, we propose an extension of the classical SEIR model by dividing infectious patients in the compartment (I) into three categories: undiagnosed infected (I), diagnosed patients who are under treatment (T) and diagnosed patients who are lost to follow-up (L). We incorporate in our model delays representing the incubation period and the time needed for treatment. We also introduce three control variables in our delayed system which represent prevention, detection and the efforts that prevent the failure of treatment. The purpose of our control strategies is to minimize the number of infected individuals and the cost of intervention. The existence of the optimal controls is investigated, and a characterization of the three controls is given using the Pontryagin's maximum principle with delays. To solve numerically the optimality system with delays, we present an adapted iterative method based on the iterative Forward-Backward Sweep Method (FBSM). Numerical simulations performed using Matlab are also provided. They indicate that the prevention control is the most effective one. To the best of our knowledge, it is the first work to apply optimal control theory to a TB model which considers infectious patients diagnosis, loss to follow-up phenomenon and multiple time delays. |
| first_indexed | 2024-04-10T12:12:32Z |
| format | Article |
| id | doaj.art-838760a9ff1d4413aded8f016e0516cf |
| institution | Directory Open Access Journal |
| issn | 2146-0957 2146-5703 |
| language | English |
| last_indexed | 2024-04-10T12:12:32Z |
| publishDate | 2021-01-01 |
| publisher | Balikesir University |
| record_format | Article |
| series | An International Journal of Optimization and Control: Theories & Applications |
| spelling | doaj.art-838760a9ff1d4413aded8f016e0516cf2023-02-15T16:15:56ZengBalikesir UniversityAn International Journal of Optimization and Control: Theories & Applications2146-09572146-57032021-01-0111110.11121/ijocta.01.2021.00885Optimal control problem for a tuberculosis model with multiple infectious compartments and time delaysMohamed Elhia0Omar Balatif1Lahoucine Boujallal2Mostafa Rachik3Hassan II UniversityChouaib Doukkali UniversityHassan II UniversityHassan II UniversityIn this paper, we formulate an optimal control problem based on a tuberculosis model with multiple infectious compartments and time delays. In order to have a more realistic model that allows highlighting the role of detection, loss to follow-up and treatment in TB transmission, we propose an extension of the classical SEIR model by dividing infectious patients in the compartment (I) into three categories: undiagnosed infected (I), diagnosed patients who are under treatment (T) and diagnosed patients who are lost to follow-up (L). We incorporate in our model delays representing the incubation period and the time needed for treatment. We also introduce three control variables in our delayed system which represent prevention, detection and the efforts that prevent the failure of treatment. The purpose of our control strategies is to minimize the number of infected individuals and the cost of intervention. The existence of the optimal controls is investigated, and a characterization of the three controls is given using the Pontryagin's maximum principle with delays. To solve numerically the optimality system with delays, we present an adapted iterative method based on the iterative Forward-Backward Sweep Method (FBSM). Numerical simulations performed using Matlab are also provided. They indicate that the prevention control is the most effective one. To the best of our knowledge, it is the first work to apply optimal control theory to a TB model which considers infectious patients diagnosis, loss to follow-up phenomenon and multiple time delays.http://www.ijocta.org/index.php/files/article/view/885Optimal controltime delaysTuberculosisnumerical simulations |
| spellingShingle | Mohamed Elhia Omar Balatif Lahoucine Boujallal Mostafa Rachik Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays An International Journal of Optimization and Control: Theories & Applications Optimal control time delays Tuberculosis numerical simulations |
| title | Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays |
| title_full | Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays |
| title_fullStr | Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays |
| title_full_unstemmed | Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays |
| title_short | Optimal control problem for a tuberculosis model with multiple infectious compartments and time delays |
| title_sort | optimal control problem for a tuberculosis model with multiple infectious compartments and time delays |
| topic | Optimal control time delays Tuberculosis numerical simulations |
| url | http://www.ijocta.org/index.php/files/article/view/885 |
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