WITHDRAWN: Nonlinear ODE mathematical analysis of the insulin-glucose model in the presence of a condition in glycemia function H(G).

Abstract

This work aims to analyze a fifth-order nonlinear ordinary differential equations that describe the glucoregulatory model system based on intravenous injection of glucose via in-vivo experimentation in rats reported previously in the literature. A mathematical analysis shows that existence of an invariant plane condition associated with insulin can determine a type 1 or type 2 diabetes classification. The bounded positive invariant domain (BPID) by applying the Lyapunov direct method establishes a mathematical preamble where maximum cell population is associated to an upper bound set given by a localizing function by applying the LCIS (Localizing Compact Invariant Set) method. Furthermore, an equilibrium point's existing condition is defined if U(t) is an invariant plane and H(G) exists. Also are discussed parameter conditions for renal glucose excretion (k5) and the rate constant of glucose absorption (ka) as a case of study when glycemia function presents existence conditions with or without insulin variable.