A fractional-order model for MINMOD Millennium.

Abstract MINMOD Millennium has been widely used to estimate insulin sensitivity ( S I ) in glucose–insulin dynamics. In order to explain the rheological behavior of glucose–insulin we attempt to modify MINMOD Millennium with fractional-order differentiation of order α ∈ (0, 1]. We show that the new modified model has non-negative, bounded solutions and a stable equilibrium point. Quasi-optimal fractional orders and parameters are estimated by using a nonlinear weighted least-squares method, the Levenberg–Marquardt algorithm, and the fractional Adams–Bashforth–Moulton method for several subjects (normal subjects and type 2 diabetic patients). The numerical results confirm that S I is significantly lower in diabetics than in non-diabetics. In addition, we explain the new factor ( τ 1 − α ) determining glucose tolerance and the relation between S I and τ 1 − α .