Analysis of physical activity effects on plasma glucose–insulin system dynamics: A mathematical model

Abstract

The main objective of this paper is to understand and analyse the effect of physical activity on plasma glucose and plasma insulin levels through mathematical modelling. Energy for the human body during physical activity is provided by glucose as sugar, while insulin as hormone supports the absorption of this glucose. Furthermore, glucose and insulin are interrelated physiologically by some parameters that we estimate mathematically by using nonlinear optimization and data collected in Rwanda. Research in this direction has been done by, for example Anirban and colleagues, who developed a dynamic model of exercise effect on plasma glucose and insulin levels. As a benchmark, the results of numerical simulation obtained in this paper have been compared with those of Anirban and colleagues to test the efficiency of our mathematical model. We have concluded that the results of those two separate mathematical models are in good accordance and that the proposed mathematical model allows further investigation of the effects of physical activity on the dynamics of the glucose–insulin system. Moreover, we have implemented a particle filtering algorithm for estimation of glucose and insulin in internal parts of the body such as heart and liver by using measurements from peripheral tissues as noisy data because taking blood samples from all parts of the body is practically and clinically impossible.