Analysis of the dynamics and optimal control of cutaneous Leishmania during human immigration
Leishmania is an infectious disease that is difficult to control and has an impact on morbidity and mortality around the world. This study investi-gates the dynamics of cutaneous Leishmania and optimal control measures, particularly in regards to human immigration. Applying a mathematical model to e...
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| Format: | Article |
| Language: | English |
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Ferdowsi University of Mashhad
2025-03-01
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| Series: | Iranian Journal of Numerical Analysis and Optimization |
| Subjects: | |
| Online Access: | https://ijnao.um.ac.ir/article_45719_080163890b44d41c2481a86331ea4669.pdf |
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| author | H. Toufga A. Sakkoum L. Benahmadi M. Lhous |
| author_facet | H. Toufga A. Sakkoum L. Benahmadi M. Lhous |
| author_sort | H. Toufga |
| collection | DOAJ |
| description | Leishmania is an infectious disease that is difficult to control and has an impact on morbidity and mortality around the world. This study investi-gates the dynamics of cutaneous Leishmania and optimal control measures, particularly in regards to human immigration. Applying a mathematical model to evaluate the dynamics of human immigration and sand flies pop-ulation. The human population is classified into four compartments: sus-ceptible, exposed, infectious, and recovered. The sand fly population is divided into three categories: susceptible, exposed, and infectious. The mathematical analysis involves positivity, existence and the uniqueness of the solution. We analyzed the global stability of the system around the endemic equilibrium point by contracting the Lyapunov function. Optimal control measures are used to reduce the number of infected and exposed individuals among humans, sand flies, and migrants. These techniques are described using Pontryagin’s Maximum Principle to derive necessary conditions for optimal control. The numerical simulations confirm the the-oretical results by showing that following these controls effectively reduces the spread of the disease, and immigration has a major impact on the spread of human-borne Leishmania. |
| format | Article |
| id | doaj-art-0d9fafac273240e7860be56bdfede370 |
| institution | OA Journals |
| issn | 2423-6977 2423-6969 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | Ferdowsi University of Mashhad |
| record_format | Article |
| series | Iranian Journal of Numerical Analysis and Optimization |
| spelling | doaj-art-0d9fafac273240e7860be56bdfede3702025-08-20T02:13:39ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692025-03-0115Issue 131134510.22067/ijnao.2024.88709.146645719Analysis of the dynamics and optimal control of cutaneous Leishmania during human immigrationH. Toufga0A. Sakkoum1L. Benahmadi2M. Lhous3Fundamental and Applied Mathematics Laboratory (FAML), Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, Morocco.Fundamental and Applied Mathematics Laboratory (FAML), Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, Morocco.Fundamental and Applied Mathematics Laboratory (FAML), Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, Morocco.Fundamental and Applied Mathematics Laboratory (FAML), Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, Morocco.Leishmania is an infectious disease that is difficult to control and has an impact on morbidity and mortality around the world. This study investi-gates the dynamics of cutaneous Leishmania and optimal control measures, particularly in regards to human immigration. Applying a mathematical model to evaluate the dynamics of human immigration and sand flies pop-ulation. The human population is classified into four compartments: sus-ceptible, exposed, infectious, and recovered. The sand fly population is divided into three categories: susceptible, exposed, and infectious. The mathematical analysis involves positivity, existence and the uniqueness of the solution. We analyzed the global stability of the system around the endemic equilibrium point by contracting the Lyapunov function. Optimal control measures are used to reduce the number of infected and exposed individuals among humans, sand flies, and migrants. These techniques are described using Pontryagin’s Maximum Principle to derive necessary conditions for optimal control. The numerical simulations confirm the the-oretical results by showing that following these controls effectively reduces the spread of the disease, and immigration has a major impact on the spread of human-borne Leishmania.https://ijnao.um.ac.ir/article_45719_080163890b44d41c2481a86331ea4669.pdfleishmaniamathematical modelimmigrationstabilityopti-mal control |
| spellingShingle | H. Toufga A. Sakkoum L. Benahmadi M. Lhous Analysis of the dynamics and optimal control of cutaneous Leishmania during human immigration Iranian Journal of Numerical Analysis and Optimization leishmania mathematical model immigration stability opti-mal control |
| title | Analysis of the dynamics and optimal control of cutaneous Leishmania during human immigration |
| title_full | Analysis of the dynamics and optimal control of cutaneous Leishmania during human immigration |
| title_fullStr | Analysis of the dynamics and optimal control of cutaneous Leishmania during human immigration |
| title_full_unstemmed | Analysis of the dynamics and optimal control of cutaneous Leishmania during human immigration |
| title_short | Analysis of the dynamics and optimal control of cutaneous Leishmania during human immigration |
| title_sort | analysis of the dynamics and optimal control of cutaneous leishmania during human immigration |
| topic | leishmania mathematical model immigration stability opti-mal control |
| url | https://ijnao.um.ac.ir/article_45719_080163890b44d41c2481a86331ea4669.pdf |
| work_keys_str_mv | AT htoufga analysisofthedynamicsandoptimalcontrolofcutaneousleishmaniaduringhumanimmigration AT asakkoum analysisofthedynamicsandoptimalcontrolofcutaneousleishmaniaduringhumanimmigration AT lbenahmadi analysisofthedynamicsandoptimalcontrolofcutaneousleishmaniaduringhumanimmigration AT mlhous analysisofthedynamicsandoptimalcontrolofcutaneousleishmaniaduringhumanimmigration |