Abstract
In this paper, we are interested in looking for Hopf bifurcation solutions for mathematical model of plasma glucose and insulin during physical activity. The mathematical model is governed by a system of delay differential equations. The algorithm for determining the critical delays that are appropriate for Hopf bifurcation is used. The illustrative example is taken for a 30 years old woman who practices regular three types of physical activity: walking, jogging and running fast.
Highlights
It is known by physicians that lifestyle factors largely influence our health
We focus on the mathematical model presented in [18] where we add two positive delays and we are interested in its Hopf bifurcation
Two positive delays are added in bi-compartmental mathematical model presented in [18] for showing the role of physical activity in controlling the plasma glucose level and in improving insulin sensitivity
Summary
It is known by physicians that lifestyle factors largely influence our health. These factors are diet, physical activity, smoking and psychological stress. (2014) Hopf Bifurcation of a Two Delay Mathematical Model of Glucose and Insulin during Physical Activity. It is essential to highlight the role played by the physical activity to Type 2 diabetes where there is low plasma insulin to an intravenous glucose challenge. Since the 1960s, mathematical models have been developed to describe glucose-insulin dynamics [8] [13]. A mathematical model has been developed to capture the integral impact of physical activity to glucose and insulin [18]. All these mathematical models are governed by ordinary differential equations but they do not consider the delays.
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