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

Lei Zhang; Basem Al Alwan; Ahmed Alshehri; Wojciech Sumelka

doi:10.1016/j.rinp.2021.104971

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Artykuł

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Tytuł

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

Autorzy

Lei Zhang
Basem Al Alwan
Ahmed Alshehri
Wojciech Sumelka (WILiT) ^{[ 1 ][ 2.7 ][ P ]}

^{[ 1 ]} Instytut Analizy Konstrukcji, Wydział Inżynierii Lądowej i Transportu, Politechnika Poznańska | ^{[ P ]} pracownik

Dyscyplina naukowa (Ustawa 2.0)

[2.7] Inżynieria lądowa i transport

Rok publikacji

2021

Opublikowano w

Results in Physics

Rocznik: 2021 | Tom: vol. 31

Typ artykułu

artykuł naukowy

Język publikacji

angielski

Słowa kluczowe

EN

Optimal control theory
Data fitting
COVID-19
Global sensitivity analysis

Streszczenie

EN 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.

Data udostępnienia online

12.11.2021

Strony (od-do)

104971-1 - 104971-9

DOI

10.1016/j.rinp.2021.104971

URL

https://www.sciencedirect.com/science/article/pii/S2211379721009840

Uwagi

Article Number: 104971

Typ licencji

CC BY-NC-ND (uznanie autorstwa - użycie niekomercyjne - bez utworów zależnych)