Mathematical model for the dynamics of β – 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-glu
cose kinetics incorporating the effect of cortisol, epinephrine, and physiological delay. 
Parameter ρc
 is define and incorporated in this work to represent the effectiveness of 
cortisol in suppressing insulin, also the parameter Gc
(t – τ) is define and incorporated to 
represent cortisol induced glucose increase with τ 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 cor
tisol 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.