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arXiv · 2403.00364

Optimal Control of a Diffusive Epidemiological Model Involving the Caputo-Fabrizio Fractional Time-Derivative

Achraf Zinihi·Moulay Rchid Sidi Ammi·Matthias Ehrhardt
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Abstract

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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Achraf Zinihi, Moulay Rchid Sidi Ammi, Matthias Ehrhardt. 2024-03-01. Optimal Control of a Diffusive Epidemiological Model Involving the Caputo-Fabrizio Fractional Time-Derivative. https://doi.org/10.1016/j.padiff.2025.101188

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