Optimal Control of a Diffusive Epidemiological Model Involving the Caputo-Fabrizio Fractional Time-Derivative
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909606559612928 |
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| author | Zinihi, Achraf Ammi, Moulay Rchid Sidi Ehrhardt, Matthias |
| author_facet | Zinihi, Achraf Ammi, Moulay Rchid Sidi Ehrhardt, Matthias |
| contents | 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_00364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal Control of a Diffusive Epidemiological Model Involving the Caputo-Fabrizio Fractional Time-Derivative Zinihi, Achraf Ammi, Moulay Rchid Sidi Ehrhardt, Matthias Dynamical Systems 92C60, 26A33, 34K08, 33F05, 49J20 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. |
| title | Optimal Control of a Diffusive Epidemiological Model Involving the Caputo-Fabrizio Fractional Time-Derivative |
| topic | Dynamical Systems 92C60, 26A33, 34K08, 33F05, 49J20 |
| url | https://arxiv.org/abs/2403.00364 |