Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function

Abstract In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana–Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium point...

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Main Authors:	Amir Khan, Rahat Zarin, Usa Wannasingha Humphries, Ali Akgül, Anwar Saeed, Taza Gul
Format:	Article
Language:	English
Published:	SpringerOpen 2021-08-01
Series:	Advances in Difference Equations
Subjects:	Pandemic model Mittag-Leffler function Stability analysis Optimal control Sensitivity analysis Numerical simulations
Online Access:	https://doi.org/10.1186/s13662-021-03546-y

id	doaj-df189cf418ea44ffb412e7a6c6fa629e
record_format	Article
spelling	doaj-df189cf418ea44ffb412e7a6c6fa629e2021-08-22T11:12:00ZengSpringerOpenAdvances in Difference Equations1687-18472021-08-012021112210.1186/s13662-021-03546-yFractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler functionAmir Khan0Rahat Zarin1Usa Wannasingha Humphries2Ali Akgül3Anwar Saeed4Taza Gul5Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology, Thonburi (KMUTT)Department of Basic Sciences, University of Engineering and TechnologyDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology, Thonburi (KMUTT)Department of Mathematics, Art and Science Faculty of Science, Siirt UniversityCenter of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT)Mathematics Department, City University of Science and Information TechnologyAbstract In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana–Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray–Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik–Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.https://doi.org/10.1186/s13662-021-03546-yPandemic modelMittag-Leffler functionStability analysisOptimal controlSensitivity analysisNumerical simulations
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Amir Khan Rahat Zarin Usa Wannasingha Humphries Ali Akgül Anwar Saeed Taza Gul
spellingShingle	Amir Khan Rahat Zarin Usa Wannasingha Humphries Ali Akgül Anwar Saeed Taza Gul Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function Advances in Difference Equations Pandemic model Mittag-Leffler function Stability analysis Optimal control Sensitivity analysis Numerical simulations
author_facet	Amir Khan Rahat Zarin Usa Wannasingha Humphries Ali Akgül Anwar Saeed Taza Gul
author_sort	Amir Khan
title	Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function
title_short	Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function
title_full	Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function
title_fullStr	Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function
title_full_unstemmed	Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function
title_sort	fractional optimal control of covid-19 pandemic model with generalized mittag-leffler function
publisher	SpringerOpen
series	Advances in Difference Equations
issn	1687-1847
publishDate	2021-08-01
description	Abstract In this paper, we consider a fractional COVID-19 epidemic model with a convex incidence rate. The Atangana–Baleanu fractional operator in the Caputo sense is taken into account. We establish the equilibrium points, basic reproduction number, and local stability at both the equilibrium points. The existence and uniqueness of the solution are proved by using Banach and Leray–Schauder alternative type theorems. For the fractional numerical simulations, we use the Toufik–Atangana scheme. Optimal control analysis is carried out to minimize the infection and maximize the susceptible people.
topic	Pandemic model Mittag-Leffler function Stability analysis Optimal control Sensitivity analysis Numerical simulations
url	https://doi.org/10.1186/s13662-021-03546-y
work_keys_str_mv	AT amirkhan fractionaloptimalcontrolofcovid19pandemicmodelwithgeneralizedmittaglefflerfunction AT rahatzarin fractionaloptimalcontrolofcovid19pandemicmodelwithgeneralizedmittaglefflerfunction AT usawannasinghahumphries fractionaloptimalcontrolofcovid19pandemicmodelwithgeneralizedmittaglefflerfunction AT aliakgul fractionaloptimalcontrolofcovid19pandemicmodelwithgeneralizedmittaglefflerfunction AT anwarsaeed fractionaloptimalcontrolofcovid19pandemicmodelwithgeneralizedmittaglefflerfunction AT tazagul fractionaloptimalcontrolofcovid19pandemicmodelwithgeneralizedmittaglefflerfunction
_version_	1721200038711918592

Fractional optimal control of COVID-19 pandemic model with generalized Mittag-Leffler function

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