Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory

The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The COVID-19 is one of the deadliest pandemics in history due to its high mortality rate in a short period. Many approaches have been adopted for disease minimization and eradication. In this pape...

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Autores principales:	Lei Zhang, Saif Ullah, Basem Al Alwan, Ahmed Alshehri, Wojciech Sumelka
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Optimal control theory Data fitting COVID-19 Global sensitivity analysis Physics QC1-999
Acceso en línea:	https://doaj.org/article/e8dd29a63c7a4e8d804f6b3c1c9d38ef
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spelling	oai:doaj.org-article:e8dd29a63c7a4e8d804f6b3c1c9d38ef2021-11-20T05:05:41ZMathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory2211-379710.1016/j.rinp.2021.104971https://doaj.org/article/e8dd29a63c7a4e8d804f6b3c1c9d38ef2021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2211379721009840https://doaj.org/toc/2211-3797The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The COVID-19 is one of the deadliest pandemics in history due to its high mortality rate in a short period. Many approaches have been adopted for disease minimization and eradication. In this paper, we studied the impact of various constant and time-dependent variable control measures coupled with vaccination on the dynamics of COVID-19. The optimal control theory is used to optimize the model and set an effective control intervention for the infection. Initially, we formulate the mathematical epidemic model for the COVID-19 without variable controls. The model basic mathematical assessment is presented. The nonlinear least-square procedure is utilized to parameterize the model from actual cases reported in Pakistan. A well-known technique based on statistical tools known as the Latin-hypercube sampling approach (LHS) coupled with the partial rank correlation coefficient (PRCC) is applied to present the model global sensitivity analysis. Based on global sensitivity analysis, the COVID-19 vaccine model is reformulated to obtain a control problem by introducing three time dependent control variables for isolation, vaccine efficacy and treatment enhancement represented by u1(t), u2(t)and u3(t), respectively. The necessary optimality conditions of the control problem are derived via the optimal control theory. Finally, the simulation results are depicted with and without variable controls using the well-known Runge–Kutta numerical scheme. The simulation results revealed that time-dependent control measures play a vital role in disease eradication.Lei ZhangSaif UllahBasem Al AlwanAhmed AlshehriWojciech SumelkaElsevierarticleOptimal control theoryData fittingCOVID-19Global sensitivity analysisPhysicsQC1-999ENResults in Physics, Vol 31, Iss , Pp 104971- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Optimal control theory Data fitting COVID-19 Global sensitivity analysis Physics QC1-999
spellingShingle	Optimal control theory Data fitting COVID-19 Global sensitivity analysis Physics QC1-999 Lei Zhang Saif Ullah Basem Al Alwan Ahmed Alshehri Wojciech Sumelka Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory
description	The coronavirus infectious disease (COVID-19) is a novel respiratory disease reported in 2019 in China. The COVID-19 is one of the deadliest pandemics in history due to its high mortality rate in a short period. Many approaches have been adopted for disease minimization and eradication. In this paper, we studied the impact of various constant and time-dependent variable control measures coupled with vaccination on the dynamics of COVID-19. The optimal control theory is used to optimize the model and set an effective control intervention for the infection. Initially, we formulate the mathematical epidemic model for the COVID-19 without variable controls. The model basic mathematical assessment is presented. The nonlinear least-square procedure is utilized to parameterize the model from actual cases reported in Pakistan. A well-known technique based on statistical tools known as the Latin-hypercube sampling approach (LHS) coupled with the partial rank correlation coefficient (PRCC) is applied to present the model global sensitivity analysis. Based on global sensitivity analysis, the COVID-19 vaccine model is reformulated to obtain a control problem by introducing three time dependent control variables for isolation, vaccine efficacy and treatment enhancement represented by u1(t), u2(t)and u3(t), respectively. The necessary optimality conditions of the control problem are derived via the optimal control theory. Finally, the simulation results are depicted with and without variable controls using the well-known Runge–Kutta numerical scheme. The simulation results revealed that time-dependent control measures play a vital role in disease eradication.
format	article
author	Lei Zhang Saif Ullah Basem Al Alwan Ahmed Alshehri Wojciech Sumelka
author_facet	Lei Zhang Saif Ullah Basem Al Alwan Ahmed Alshehri Wojciech Sumelka
author_sort	Lei Zhang
title	Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory
title_short	Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory
title_full	Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory
title_fullStr	Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory
title_full_unstemmed	Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory
title_sort	mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: an application of optimal control theory
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/e8dd29a63c7a4e8d804f6b3c1c9d38ef
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Mathematical assessment of constant and time-dependent control measures on the dynamics of the novel coronavirus: An application of optimal control theory

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