Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction

Abstract

Abstract This paper proposes a fractional-order model of glucose–insulin interaction. In Caputo’s meaning, the fractional derivative is defined. This model arises in Bergman’s minimal model, used to describe blood glucose and insulin metabolism, after intravenous tolerance testing. We showed that the established model has existence, uniqueness, non-negativity, and boundedness of fractional-order model solutions. The model’s local and global stability was investigated. The parametric conditions under which a Hopf bifurcation occurs in the positive steady state for a proposed model are studied. Moreover, we present a numerical treatment for solving the proposed fractional model using the generalized Euler method (GEM). The model’s local stability and Hopf bifurcation of the proposed model in sense of the GEM are presented. Finally, numerical simulations of the model using the Adam–Bashforth–Moulton predictor corrector scheme and the GEM have been presented to support our analytical results.