Mathematical Model for the Dynamics of beta-cell Mass, Insulin-Glucose Kinetics Incorporating the Effect of Cortisol, Epinephrine and Physiological Delay

Abstract

This work presents a mathematical model for the dynamics of β-cell mass, insulin-glucose kinetics incorporating the effect of cortisol, epinephrine and physiological delay. Parameter is define and incorporated in this work to represent the effectiveness of cortisol in suppressing insulin, also the parameter is define and incorporated to represent cortisol induced glucose increase with representing physiological delay as the factor that affect glucose-insulin homeostasis. The model consists of a system of three non-linear ordinary differential equations. The model is use to investigate the combine effect of cortisol and epinephrine with physiological delay on; glucose, insulin and beta-cell mass dynamics. The results of the study show that: In the combined presence of cortisol and epinephrine, the blood glucose increase more and the blood insulin decrease due to suppression by the hormone, despite the fact that there is increase in beta-cell mass, the system remains extremely hyperglycemic. The analytical results further show that continuous; stress, excitement and/or trauma lead to constant secretion of cortisol and epinephrine into the blood stream. Frequent secretion of cortisol and epinephrine increases the risk of diabetes in humans.