Investigating the glucose metabolism regulatory network through a Caputo fractional order differential model

Abstract

To model memory-dependent systems, Caputo’s fractional-order differentiation has emerged as a predominant framework within the scientific community. From prey-predator networks to complex disease dynamics in eco-epidemiology, fractional-order models represent a robustly analyzed field. Diabetes, a non-communicable metabolic disorder, exhibits dynamics that are critically dependent on long-term systemic behavior. In this study, a fractional-order model is developed and analyzed to interpret the long-term glucose metabolism regulatory network. The model incorporates four state variables: plasma glucose (G), insulin concentration (I), liver glycogen concentration (X), and glucagon concentration (P). Numerical simulations reveal rich dynamical behavior, including stable steady states, damped oscillations, and bifurcation phenomena such as Hopf and transcritical bifurcations. The fractional order (α) is shown to play a crucial role in governing system dynamics, where intermediate values yield results that are most physiologically consistent. This study provides insights into the long-term behavior of the diabetic pathway, thereby enhancing the understanding of complex glucose metabolism and its underlying regulatory mechanisms.