The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission

This study examines the mathematical model of Hepatitis B Virus (HBV) dynamics, focusing on its various stages of infection, including acute and chronic phases, and transmission pathways. By utilizing mathematical modeling and fractional calculus techniques with the Θ-Hilfer operator, we analyze the...

Full description

Saved in:
Bibliographic Details
Main Authors: K. Ramalakshmi, B. Sundara Vadivoo, Kottakkaran Sooppy Nisar, Suliman Alsaeed
Format: Article
Language:English
Published: Elsevier 2024-12-01
Series:Results in Control and Optimization
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S2666720724001267
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1850251544687017984
author K. Ramalakshmi
B. Sundara Vadivoo
Kottakkaran Sooppy Nisar
Suliman Alsaeed
author_facet K. Ramalakshmi
B. Sundara Vadivoo
Kottakkaran Sooppy Nisar
Suliman Alsaeed
author_sort K. Ramalakshmi
collection DOAJ
description This study examines the mathematical model of Hepatitis B Virus (HBV) dynamics, focusing on its various stages of infection, including acute and chronic phases, and transmission pathways. By utilizing mathematical modeling and fractional calculus techniques with the Θ-Hilfer operator, we analyze the epidemic’s behavior. The research proposes control strategies, such as treatment and vaccination, aimed at reducing both acute and chronic infections. To achieve optimal control, we employ Pontryagin’s Maximum Principle. Through simulations, we demonstrate the effectiveness of our approach using the Non-Standard Two-Step Lagrange Interpolation Method (NS2LIM), supported by numerical findings and graphical representations. Additionally, we identify two control variables to minimize the populations of acute and chronic infections while enhancing recovery rates.
format Article
id doaj-art-ec5b69dbdc494828b8cdb71a6fb21fe1
institution OA Journals
issn 2666-7207
language English
publishDate 2024-12-01
publisher Elsevier
record_format Article
series Results in Control and Optimization
spelling doaj-art-ec5b69dbdc494828b8cdb71a6fb21fe12025-08-20T01:57:52ZengElsevierResults in Control and Optimization2666-72072024-12-011710049610.1016/j.rico.2024.100496The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmissionK. Ramalakshmi0B. Sundara Vadivoo1Kottakkaran Sooppy Nisar2Suliman Alsaeed3Department of Mathematics, Alagappa University, Karaikudi 630 004, IndiaDepartment of Mathematics, Central University of Tamil Nadu, Thiruvarur 610 005, IndiaDepartment of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia; Saveetha School of Engineering, SIMATS, Chennai, India; Corresponding author at: Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia.Mathematics Department, College of Sciences, Umm Al-Qura University, Makkah, Saudi ArabiaThis study examines the mathematical model of Hepatitis B Virus (HBV) dynamics, focusing on its various stages of infection, including acute and chronic phases, and transmission pathways. By utilizing mathematical modeling and fractional calculus techniques with the Θ-Hilfer operator, we analyze the epidemic’s behavior. The research proposes control strategies, such as treatment and vaccination, aimed at reducing both acute and chronic infections. To achieve optimal control, we employ Pontryagin’s Maximum Principle. Through simulations, we demonstrate the effectiveness of our approach using the Non-Standard Two-Step Lagrange Interpolation Method (NS2LIM), supported by numerical findings and graphical representations. Additionally, we identify two control variables to minimize the populations of acute and chronic infections while enhancing recovery rates.http://www.sciencedirect.com/science/article/pii/S2666720724001267Hepatitis B virusFractional optimal control problemsΘ-Hilfer derivativeNS2LIM
spellingShingle K. Ramalakshmi
B. Sundara Vadivoo
Kottakkaran Sooppy Nisar
Suliman Alsaeed
The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission
Results in Control and Optimization
Hepatitis B virus
Fractional optimal control problems
Θ-Hilfer derivative
NS2LIM
title The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission
title_full The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission
title_fullStr The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission
title_full_unstemmed The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission
title_short The Θ-Hilfer fractional order model for the optimal control of the dynamics of Hepatitis B virus transmission
title_sort θ hilfer fractional order model for the optimal control of the dynamics of hepatitis b virus transmission
topic Hepatitis B virus
Fractional optimal control problems
Θ-Hilfer derivative
NS2LIM
url http://www.sciencedirect.com/science/article/pii/S2666720724001267
work_keys_str_mv AT kramalakshmi thethhilferfractionalordermodelfortheoptimalcontrolofthedynamicsofhepatitisbvirustransmission
AT bsundaravadivoo thethhilferfractionalordermodelfortheoptimalcontrolofthedynamicsofhepatitisbvirustransmission
AT kottakkaransooppynisar thethhilferfractionalordermodelfortheoptimalcontrolofthedynamicsofhepatitisbvirustransmission
AT sulimanalsaeed thethhilferfractionalordermodelfortheoptimalcontrolofthedynamicsofhepatitisbvirustransmission
AT kramalakshmi thhilferfractionalordermodelfortheoptimalcontrolofthedynamicsofhepatitisbvirustransmission
AT bsundaravadivoo thhilferfractionalordermodelfortheoptimalcontrolofthedynamicsofhepatitisbvirustransmission
AT kottakkaransooppynisar thhilferfractionalordermodelfortheoptimalcontrolofthedynamicsofhepatitisbvirustransmission
AT sulimanalsaeed thhilferfractionalordermodelfortheoptimalcontrolofthedynamicsofhepatitisbvirustransmission