A fractional-order model for MINMOD Millennium

MINMOD Millennium has been widely used to estimate insulin sensitivity (S-1) 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 alpha epsilon (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 S1 is significantly lower in diabetics than in non-diabetics. In addition, we explain the new factor (tau(1-alpha)) determining glucose tolerance and the relation between S-1 and tau(1-alpha). (C) 2015 Elsevier Inc. All rights reserved.