A fractional-order model for MINMOD Millennium

• MINMOD Millennium with fractional-order α ∈ (0, 1] is proposed.
• The new modified model has positive solutions and a stable equilibrium point.
• Quasi-optimal fractional orders and parameters are estimated for many data.
• Insulin sensitivity index is significantly lower in diabetics than in non-diabetics.
• We observe the new factor (τ1 − α) determining glucose tolerance.

MINMOD Millennium has been widely used to estimate insulin sensitivity (SI) 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 SI is significantly lower in diabetics than in non-diabetics. In addition, we explain the new factor (τ1 − α) determining glucose tolerance and the relation between SI and τ1 − α.