title: A fractional-order model for MINMOD Millennium.
abstract: 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 (τ(1 - α)) determining glucose tolerance and the relation between SI and τ(1 - α).
authors: Department of Mathematics, Seoul National University, Seoul 151-747, Korea. Electronic address: deux0844@snu.ac.kr.
authors: Yongjin
authors: Y
authors: Cho
authors: Department of Mathematics, Seoul National University, Seoul 151-747, Korea. Electronic address: ibkim11@gmail.com.
authors: Imbunm
authors: I
authors: Kim
authors: Department of Mathematics, Seoul National University, Seoul 151-747, Korea; Interdisciplinary Program in Computational Science & Technology, Seoul National University, Seoul 151-747, Korea. Electronic address: sheen@snu.ac.kr.
authors: Dongwoo
authors: D
authors: Sheen
mesh_terms: D005947:Glucose / Q000378:metabolism; D006801:Humans; D007328:Insulin / Q000378:metabolism; D007333:Insulin Resistance; D055641:Mathematical Concepts; D008954:Models, Biological
chemical_list: D007328:Insulin; D005947:Glucose
keywords: Diabetes; Fractional derivative; Glucose–insulin; Minimal model