A Mathematical Study of Effects of Delays Arising from The Interaction of Glucose and Insulin in The Body
Mariani (a), Rudy Kusdiantara (b)

(a) Institut Teknologi Bandung, (b) Institut Teknologi Bandung

Abstract

The interaction between glucose and insulin was modeled mathematically using a delay differential equation. The delay factor in the model states that there is a natural delay that occurs during the pancreas process of producing insulin and a natural delay that occurs during the process of glucose production in the blood to balance the body^s metabolism. The glucose-insulin interaction system with two delay factors will be investigated. By choosing \tau_1 dan \tau_2 as the bifurcation parameters, we can indicate that the Hopf bifurcation will appear when the time delay crosses some critical values. The linear stability of the steady-state point will be investigated and the Hopf bifurcation will be demonstrated by analyzing the characteristic equations of each case. Numerical simulations are given to describe the results of the analytical solution and changes in stability behavior will be observed.

Keywords: Delay differential equation, Glucose, Hopf bifurcation, Insulin, Stability analysis

Topic: MATHEMATICS AND STATISTICS