Mathematical modeling of type 1 diabetes using systems of differential equations
Dragos Arotaritei, Ilea Mihail-ovidiu
Source abstract
Type 1 diabetes mellitus is one of the most complex chronic metabolic disorders, significantly impacting both patients' quality of life and global healthcare systems. The condition is characterized by the autoimmune destruction of pancreatic β-cells, rendering the body unable to synthesize endogenous insulin. Consequently, disease management entails continuous blood glucose monitoring and ongoing insulin administration to maintain glucose levels within physiological ranges. Interest in this topic has arisen from the steadily increasing number of individuals diagnosed with type 1 diabetes and the need to develop modern methods for analyzing, predicting, and controlling glycemic fluctuations. Currently, modern technologies increasingly employ mathematical models and numerical simulations to understand pathophysiological mechanisms and to develop intelligent insulin delivery systems. This article aims to analyze the progression of type 1 diabetes mellitus through mathematical modeling based on differential equation-based dynamical systems. The study seeks to accurately simulate the complex interaction between glucose concentration and insulin kinetics, evaluating glycemic variations and trajectories under various physiological conditions and exogenous protocols. This approach highlights the critical role of biomathematics in deciphering the disease's time-dependent pathophysiological mechanisms, as well as in the design, optimization, and development of modern algorithms for continuous monitoring and automated glycemic control. Mathematical modeling serves as an essential tool for describing complex biological processes and conducting simulations capable of replicating the human body's physiological responses. In this context, the MATLAB platform facilitates the efficient implementation and simulation of these models, contributing to the analysis of glucose-insulin system dynamics and the comparative evaluation of various therapeutic strategies.
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