COVID-19 spatiotemporal SIR model: Regional optimal control approach

Marouane Karim, Soukaina Ben Rhila, Hamza Boutayeb, Mostafa Rachik

Abstract


In the present work, we consider a spatio-temporal model to describe the evolution of covid19 in an area Ω (Ω can be a city, a country,..). Taking into account the financial means of the considered country, we suppose that the number of available vaccines is destined to a region ω1⊆Ω (ω1 can be an industrial city, a university city...) and we suppose that the available treatments are dedicated to a region ω2⊆Ω (ω2 can be a military city,..), it is not excluded that ω12. To minimize the number of infection with minimal cost, we apply an optimal regional control strategy to stop the death of infected individuals in the considered area. Much of this work has been devoted to mathematical study, where the existence of the optimal controls and the solutions of the state system are proven, an optimal control characterization in terms of state and adjoint functions are provided, and the optimality system is solved numerically using a forward-backward sweep method. Our numerical results suggest that when vaccination and treatment procedures are used together, the control approach becomes more effective in protecting a specific region from epidemic transmission from neighboring regions.

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Published: 2022-11-07

How to Cite this Article:

Marouane Karim, Soukaina Ben Rhila, Hamza Boutayeb, Mostafa Rachik, COVID-19 spatiotemporal SIR model: Regional optimal control approach, Commun. Math. Biol. Neurosci., 2022 (2022), Article ID 115

Copyright © 2022 Marouane Karim, Soukaina Ben Rhila, Hamza Boutayeb, Mostafa Rachik. 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.

Commun. Math. Biol. Neurosci.

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