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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| Format: | Article |
| Language: | English |
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Elsevier
2025-02-01
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| Series: | Alexandria Engineering Journal |
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| 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. |
| format | Article |
| id | doaj-art-9624cdeb463d4a3db681bd082724e0b5 |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| 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 |