Dynamics and Optimal Control Methods for the COVID-19 Model

Saida Id Ouaziz and Mohammed EL Khomssi
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Saida Id Ouaziz: Sidi Mohamed Ben Abdellah University
Mohammed EL Khomssi: Sidi Mohamed Ben Abdellah University

A chapter in Mathematical Modeling and Intelligent Control for Combating Pandemics, 2023, pp 21-38 from Springer

Abstract: Abstract Reportedly, a new variant of a virus named coronavirus has been the focus of attention in Wuhan in December 2019. This virus has emerged globally, affecting many nations around the world. In this chapter, mathematical modeling and data analysis are used to comprehend the effect of COVID-19 on society. We represent a deterministic mathematical model of the COVID-19 pandemic as an infectious disease. The dynamics of the interaction between the compartments are formally described by five ODEs. We prove the existence and uniqueness of the solution to our problem by utilizing the fixed point theorem. The equilibrium points are determined. We infer that the model exhibits both disease-free and endemic steady states. We have exposed the stability of these equilibria at the local and global scales. Also, the parameter’s sensitivity analysis is carried out, and as a consequence, our discussed model provides a good approximation of the actual COVID-19 data. A stay-at-home order, a travel ban, and solitary confinement are offered as realistic and suitable control techniques to prevent and stop the propagation of the COVID-19 virus hand in hand with the optimal control approach which is based on the model of the 2019 Coronavirus (COVID-19). The optimal controls have been described using Pontryagin’s maximal principle, and the optimality system has been established. Finally, using Matlab, the theoretical study is confirmed with certain digital simulations.

Keywords: COVID-19 model; Local stability; Optimal control (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-33183-1_2

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DOI: 10.1007/978-3-031-33183-1_2

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