Order estimation for a fractional Brownian motion model of glucose control - Panunzi, Simona; Borri, Alessandro; D’Orsi, Laura; De Gaetano, Andrea (Communications in nonlinear science & numerical simulation, 2023)
When a subject is at rest and meals have not been eaten for a relatively long time (e.g. during the night), presumably near-constant, zero-order glucose production occurs in the liver. Glucose elimination from the bloodstream may be proportional to glycemia, with an apparently first-order, linear elimination rate. Besides glycemia itself, unobserved factors (insulinemia, other hormones) may exert second and higher order effects. Random events (sleep pattern variations, hormonal cycles) may also affect glycemia. The time-course of transcutaneously, continuously measured glycemia (CGM) thus reflects the superposition of different orders of control, together with random system error. The problem may be formalized as a fractional random walk, or fractional Brownian motion. In the present work, the order of this fractional stochastic process is estimated on night-time CGM data from one subject. •We propose a novel order estimation method for fractional stochastic models (FSDE).•We apply the method to a FSDE glucose model fitted from real CGM data.•A scheme for the approximate FSDE integration via finite increments is proposed.•Stochastic correctness of our algorithm in terms of increment covariance is proved.•The accuracy is comparable to other fractional noise integration algorithms.