A Novel Fractional-Order Approach for Modelling Glucose Regulation with Meal Spikes and Periodic Noise

Résumé

In this work, we develop a novel fractional order model for glucose-insulin-lactate dynamics in diabetic patients, incorporating both time-varying noise and meal-induced glucose spikes to enhance the realism of the system. This framework is about non-linear fractional differential equations that capture the chaotic behaviour of glucose regulation in the presence of noise and periodic fluctuations. To simulate real-world conditions, time-varying noise is introduced as physiological variability, including noise levels that fluctuate based on circadian rhythms and metabolic processes. In addition, we introduce meal spikes as a sudden increase in glucose levels, reflecting the physiological response to food intake. The glucose surge is modelled using a Gaussian function, with intensity and duration adjustable to simulate different meal patterns. The proposed model successfully captures the complex, real-world behaviour of glucose metabolism, providing insights into the effectiveness of control strategies under realistic conditions. From this approach, we offer a more comprehensive representation of the metabolic control system in diabetic patients and provide a practical method to examine intervention strategies.