Exploring Equilibrium Points Consistency in Insulin-Glucose Models for Type 1 Diabetes: A Novel Comparative Analysis

Various mathematical models depicting insulin-glucose dynamics in individuals with type 1 diabetes are prevalent in the scientific literature. These models serve the purpose of comprehending and forecasting how blood glucose levels react to a multitude of variables, including insulin treatment, carbohydrate consumption, physical exertion, and more. A model's principal objective is to faithfully replicate the patterns observed in experimental data. Equilibrium points within these models play a pivotal role. However, this paper sheds light on a critical concern: the coherence of these equilibrium points with clinical reality. Our study presents an open-loop comparative analysis of two mathematical models used in diabetes management. It is worth noting that the linear model proposed by Magdelaine is not well known than the Hovorka nonlinear model. The simulation results between the two approaches revealed a remarkable significance towards the Magdelaine model. They substantiate the static and dynamic advantages inherent to the Magdelaine model. Specifically, this model exhibits stability in its equilibrium points that align closely with clinical observations. Furthermore, its dynamics mimic blood glucose behaviour in individuals with type 1 diabetes.