Optimal control of glucose-insulin dynamics via delay differential model with fractional-order

This paper proposes a delay differential model with fractional order for glucose-insulin endocrine, metabolic regulation model, incorporating beta-cell dynamics to regulate and maintain bloodstream insulin concentration. In the model, two time delays are involved, namely δg and δι, which represent d...

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Main Authors: Fathalla A. Rihan, K. Udhayakumar
Format: Article
Language:English
Published: Elsevier 2025-02-01
Series:Alexandria Engineering Journal
Subjects:
Online Access:http://www.sciencedirect.com/science/article/pii/S1110016824015436
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author Fathalla A. Rihan
K. Udhayakumar
author_facet Fathalla A. Rihan
K. Udhayakumar
author_sort Fathalla A. Rihan
collection DOAJ
description This paper proposes a delay differential model with fractional order for glucose-insulin endocrine, metabolic regulation model, incorporating beta-cell dynamics to regulate and maintain bloodstream insulin concentration. In the model, two time delays are involved, namely δg and δι, which represent delayed insulin secretion and delayed glucose reduction. A moderate hyperglycemia results in beta-cell growth (negative feedback), while a severe hyperglycemia results in beta-cell reduction (positive feedback). When a time delay passes a bifurcation point, Hopf bifurcation occurs. It is evident from biological findings that the model exhibits periodic oscillations. Furthermore, we present an optimal control problem for external insulin infusions to minimize prolonged high blood sugar levels. Numerical simulations have validated the theoretical results.
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institution Kabale University
issn 1110-0168
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publishDate 2025-02-01
publisher Elsevier
record_format Article
series Alexandria Engineering Journal
spelling doaj-art-9624cdeb463d4a3db681bd082724e0b52024-12-03T04:28:42ZengElsevierAlexandria Engineering Journal1110-01682025-02-01114243255Optimal control of glucose-insulin dynamics via delay differential model with fractional-orderFathalla A. Rihan0K. Udhayakumar1Corresponding author.; Department of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain, 15551, United Arab EmiratesDepartment of Mathematical Sciences, College of Science, United Arab Emirates University, Al-Ain, 15551, United Arab EmiratesThis paper proposes a delay differential model with fractional order for glucose-insulin endocrine, metabolic regulation model, incorporating beta-cell dynamics to regulate and maintain bloodstream insulin concentration. In the model, two time delays are involved, namely δg and δι, which represent delayed insulin secretion and delayed glucose reduction. A moderate hyperglycemia results in beta-cell growth (negative feedback), while a severe hyperglycemia results in beta-cell reduction (positive feedback). When a time delay passes a bifurcation point, Hopf bifurcation occurs. It is evident from biological findings that the model exhibits periodic oscillations. Furthermore, we present an optimal control problem for external insulin infusions to minimize prolonged high blood sugar levels. Numerical simulations have validated the theoretical results.http://www.sciencedirect.com/science/article/pii/S1110016824015436Delay differential equationsOptimal controlGlucose-insulinStabilityChaos behaviorHopf bifurcation
spellingShingle Fathalla A. Rihan
K. Udhayakumar
Optimal control of glucose-insulin dynamics via delay differential model with fractional-order
Alexandria Engineering Journal
Delay differential equations
Optimal control
Glucose-insulin
Stability
Chaos behavior
Hopf bifurcation
title Optimal control of glucose-insulin dynamics via delay differential model with fractional-order
title_full Optimal control of glucose-insulin dynamics via delay differential model with fractional-order
title_fullStr Optimal control of glucose-insulin dynamics via delay differential model with fractional-order
title_full_unstemmed Optimal control of glucose-insulin dynamics via delay differential model with fractional-order
title_short Optimal control of glucose-insulin dynamics via delay differential model with fractional-order
title_sort optimal control of glucose insulin dynamics via delay differential model with fractional order
topic Delay differential equations
Optimal control
Glucose-insulin
Stability
Chaos behavior
Hopf bifurcation
url http://www.sciencedirect.com/science/article/pii/S1110016824015436
work_keys_str_mv AT fathallaarihan optimalcontrolofglucoseinsulindynamicsviadelaydifferentialmodelwithfractionalorder
AT kudhayakumar optimalcontrolofglucoseinsulindynamicsviadelaydifferentialmodelwithfractionalorder