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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Main Authors: Achraf Zinihi, Moulay Rchid Sidi Ammi, Matthias Ehrhardt
Format: Article
Language:English
Published: Elsevier 2025-06-01
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.
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publisher Elsevier
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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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