Optimal control of COVID-19

Nacima Moussouni; Mohamed Aliane

doi:10.11121/ijocta.01.2021.00974

Optimal control of COVID-19

Authors

Nacima Moussouni Laboratory L2CSP,University Mouloud Mammeri of Tizi Ouzou, 15000, Tizi-Ouzou, Algeria https://orcid.org/0000-0002-3570-2462
Mohamed Aliane Laboratory of Pure and Applied Mathematics, University Amar Telidji of Laghouat, Bp 37G, Ghardaia Road, 03000, Laghouat, Algeria https://orcid.org/0000-0002-8020-4649

DOI:

https://doi.org/10.11121/ijocta.01.2021.00974

Keywords:

Covid19, epidemic, optimal control, shooting Method, Euler Discretization Method

Abstract

Coronavirus disease of 2019 or COVID-19 (acronym for coronavirus disease 2019) is an emerging infectious disease caused by a strain of coronavirus called SARS-CoV-22, contagious with human-to-human transmission via respiratory droplets or by touching contaminated surfaces then touching them face. Faced with what the world lives, to define this problem, we have modeled it as an optimal control problem based on the models of William Ogilvy Kermack et Anderson Gray McKendrick, called SEIR model, modified by adding compartments suitable for our study. Our objective in this work is to maximize the number of recovered people while minimizing the number of infected. We solved the problem theoretically using the Pontryagin maximum principle, numerically we used and compared results of two methods namely the indirect method (shooting method) and the Euler discretization method, implemented in MATLAB.

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Author Biographies

Nacima Moussouni, Laboratory L2CSP,University Mouloud Mammeri of Tizi Ouzou, 15000, Tizi-Ouzou, Algeria

received her PhD in Mathematics at the University of Tizi-Ouzou, Algeria. She is an Associate Professor at the University of Laghouat, Algeria and the university of Orlean in France(MAPMO laboratory). Her research interests include optimal control and its applications.

Mohamed Aliane, Laboratory of Pure and Applied Mathematics, University Amar Telidji of Laghouat, Bp 37G, Ghardaia Road, 03000, Laghouat, Algeria

received his Master Degree in Analysis and Mathematical Modelling at the University of Medea, Algeria. He is a PhD student at the Department of Mathematics, University of Laghouat, Algeria. His research interests include optimal control and its applications.

References

Kermack, W.O., & McKendrick, A.G. (1927). Contributions to the mathematical theory of epidemics, part i. Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, 115, 700-721.

Goncalves, J.N.C., Rodrigues, H.S., & Mon- teiro, M.T.T. (2018). On the dynamics of a viral marketing model with optimal control using indirect and direct methods. Statistics, Optimization & Information Computing, 6, 633-644.

Rosa, S., & Torres, D.F.M. (2018). Parameter Estimation, Sensitivity Analysis and Optimal Control of a Periodic Epidemic Model with Application to HRSV in Florida. Statistics, Optimization & Information Computing, 6, 139-149.

Trelat, E. (2005). Optimal control: theory and applications. Vuibert, Concrete mathematics collection, Paris.

Moussouni, N., & Aidene, M. (2011). An Algorithm for Optimization of Cereal Output. Acta Applicandae Mathematicae, 11, 113-127.

Moussouni, N., & Aidene, M. (2016). Optimization of cereal output in presence of locusts. An International Journal of Optimization and Control: Theories & Applications, 6, 1-10.

Aliane, M., Moussouni, N., & Bentobache, M. (2020). Optimal control of a rectilinear motion of a rocket. Statistics, Optimization & Information Computing, 8, 281-295.

Aliane, M., Moussouni, N., & Bentobache, M. (2019). Nonlinear optimal control of the heel angle of a rocket. 6th International Conference on Control, Decision and Information Technologies (CODIT’19), Paris, 756-760.

Pontryagin, L.S., Boltyanskii, V.G., Gamkrelidze, R.V., & Mishchenko, E.F. (1962). The mathematical theory of optimal processes. Intersciences Publisher, New York.

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Published

2021-01-30

CITATION

DOI: 10.11121/ijocta.01.2021.00974

Published: 2021-01-30

How to Cite

Moussouni, N., & Aliane, M. (2021). Optimal control of COVID-19. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 11(1), 114–122. https://doi.org/10.11121/ijocta.01.2021.00974

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Issue

Vol. 11 No. 1 (2021): IJOCTA

Section

Research Articles

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