Optimal control of a diffusive epidemiological model involving the Caputo–Fabrizio fractional time-derivative
In this work we study a fractional SEIR biological model of a reaction–diffusion, using the non-singular kernel Caputo–Fabrizio fractional derivative in the Caputo sense and employing the Laplacian operator. In our PDE model, the government seeks immunity through the vaccination program, which is co...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-06-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818125001159 |
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| author | Achraf Zinihi Moulay Rchid Sidi Ammi Matthias Ehrhardt |
| author_facet | Achraf Zinihi Moulay Rchid Sidi Ammi Matthias Ehrhardt |
| author_sort | Achraf Zinihi |
| collection | DOAJ |
| description | In this work we study a fractional SEIR biological model of a reaction–diffusion, using the non-singular kernel Caputo–Fabrizio fractional derivative in the Caputo sense and employing the Laplacian operator. In our PDE model, the government seeks immunity through the vaccination program, which is considered a control variable. Our study aims to identify the ideal control pair that reduces the number of infected/infectious people and the associated vaccine and treatment costs over a limited time and space. Moreover, by using the forward–backward algorithm, the approximate results are explained by dynamic graphs to monitor the effectiveness of vaccination. |
| format | Article |
| id | doaj-art-5aa06dea866f4a76a86b41eb3b49772d |
| institution | OA Journals |
| issn | 2666-8181 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-5aa06dea866f4a76a86b41eb3b49772d2025-08-20T02:28:37ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812025-06-011410118810.1016/j.padiff.2025.101188Optimal control of a diffusive epidemiological model involving the Caputo–Fabrizio fractional time-derivativeAchraf Zinihi0Moulay Rchid Sidi Ammi1Matthias Ehrhardt2Department of Mathematics, MAIS Laboratory, AMNEA Group, Faculty of Sciences and Technics, Moulay Ismail University of Meknes, Errachidia 52000, MoroccoDepartment of Mathematics, MAIS Laboratory, AMNEA Group, Faculty of Sciences and Technics, Moulay Ismail University of Meknes, Errachidia 52000, MoroccoUniversity of Wuppertal, Chair of Applied and Computational Mathematics, Gaußstrasse 20, 42119 Wuppertal, Germany; Corresponding author.In this work we study a fractional SEIR biological model of a reaction–diffusion, using the non-singular kernel Caputo–Fabrizio fractional derivative in the Caputo sense and employing the Laplacian operator. In our PDE model, the government seeks immunity through the vaccination program, which is considered a control variable. Our study aims to identify the ideal control pair that reduces the number of infected/infectious people and the associated vaccine and treatment costs over a limited time and space. Moreover, by using the forward–backward algorithm, the approximate results are explained by dynamic graphs to monitor the effectiveness of vaccination.http://www.sciencedirect.com/science/article/pii/S2666818125001159Epidemiological modelFractional derivativesFractional differential equationsNumerical simulationsOptimal control |
| spellingShingle | Achraf Zinihi Moulay Rchid Sidi Ammi Matthias Ehrhardt Optimal control of a diffusive epidemiological model involving the Caputo–Fabrizio fractional time-derivative Partial Differential Equations in Applied Mathematics Epidemiological model Fractional derivatives Fractional differential equations Numerical simulations Optimal control |
| title | Optimal control of a diffusive epidemiological model involving the Caputo–Fabrizio fractional time-derivative |
| title_full | Optimal control of a diffusive epidemiological model involving the Caputo–Fabrizio fractional time-derivative |
| title_fullStr | Optimal control of a diffusive epidemiological model involving the Caputo–Fabrizio fractional time-derivative |
| title_full_unstemmed | Optimal control of a diffusive epidemiological model involving the Caputo–Fabrizio fractional time-derivative |
| title_short | Optimal control of a diffusive epidemiological model involving the Caputo–Fabrizio fractional time-derivative |
| title_sort | optimal control of a diffusive epidemiological model involving the caputo fabrizio fractional time derivative |
| topic | Epidemiological model Fractional derivatives Fractional differential equations Numerical simulations Optimal control |
| url | http://www.sciencedirect.com/science/article/pii/S2666818125001159 |
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