Enhancing blood glucose control through the fixed point theorem
DOI: https://doi.org/10.3846/mma.2025.22147Abstract
Diabetes is a chronic condition that poses significant health risks globally, arising from the body’s inability to effectively utilize insulin produced by the pancreas or insufficient insulin production. This paper proposes a novel approach to diabetes management by focusing on optimal control strategies aimed at regulating blood glucose levels to achieve desired targets. We integrate concepts of output controllability into a discrete-time model that captures the dynamics of glucose and insulin interactions. Applying fixed-point theorems, we define permissible control mechanisms for dealing with the challenge of keeping glucose concentrations within optimal ranges. The theoretical framework is supported by numerical simulations that demonstrate the efficacy of the suggested optimal control method in minimizing blood glucose fluctuations. Our findings shed light on the development of advanced blood glucose control systems, eventually leading to enhanced diabetes management and improved quality of life for individuals impacted by the disease.
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diabetes, glucose regulation, insulin, fixed-point theorems, optimal control strategiesHow to Cite
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