Control of a reaction-diffusion system: application on a SEIR epidemic mode
Abstract
In this work, we are interested in the study of a spatiotemporal SEIR epidemiological model, with no-flux boundary conditions. This model includes a constant inflow of new susceptible, exposed, infectious and recovered. In addition, it also incorporates a contact rate depending on the size of the population and another death related to the disease. Our objective is to characterize the optimal control pair, which minimizes exposed, infected individuals and the corresponding effort and treatment costs. We have demonstrated the existence of the state system solution and optimal control. The characterization of the optimal control pair is determined in terms of state functions and adjoint functions. The numerical resolution of the optimal system, has shown the effectiveness of our adopted strategy.
Copyright © 2021 Amine Alabkari, Ahmed Kourrad, Khalid Adnaoui, Adil El Alami Laaroussi, Naima Soukher, Abdelkarim Bennar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
A. Alabkari, A. Kourrad, K. Adnaoui, A. E. A. Laaroussi, N. Soukher, A. Bennar, Control of a reaction-diffusion system: application on a SEIR epidemic mode, J. Math. Comput. Sci. 11 (2021), 1601–1628. https://doi.org/10.28919/jmcs/5364
BibTeX
@article{Alabkari2021,
author = {Alabkari, Amine and Kourrad, Ahmed and Adnaoui, Khalid and Laaroussi, Adil El Alami and Soukher, Naima and Bennar, Abdelkarim},
title = {Control of a reaction-diffusion system: application on a SEIR epidemic mode},
journal = {J. Math. Comput. Sci.},
volume = {11},
year = {2021},
pages = {1601--1628},
doi = {10.28919/jmcs/5364}
}