Mathematical Model for the Dynamics of Glucose, Insulin and β-Cell Mass under the Effect of Trauma, Excitement and Stress

Abstract

In this work, we presented a mathematical model for the dynamics of glucose, insulin and beta-cell mass under the influence of trauma, excitement and/or stress, the model is an improvement on the work by [1]. We defined and incorporated a parameter  to represent the effectiveness of epinephrine in suppressing insulin secretion and a parameter Ge representing epinephrine induced glucose increase as the factors that affect glucose and insulin homeostasis. The model which consists of a system of three nonlinear ordinary differential equations was used to investigate the effect of epinephrine on glucose, insulin and beta-cell mass dynamics. The result of the study showed that; In the presence of epinephrine, the blood glucose increased and the blood insulin decreased due to suppression by the hormone, despite the fact that there is an increase in beta-cell mass the system remained extremely hyperglycemic. Furthermore, the result of the numerical experiment carried out indicated that frequent epinephrine secretion into the blood induced prolong and extreme hyperglycemia. Frequent epinephrine secretion increases the risk of diabetes in humans. In view of the findings of this study, we recommend that there should be massive and continuous health education, especially for communities living in the areas where the stated agents (trauma, excitement and stress) of epinephrine secretion are common.