Mathematical Modelling and Simulation of &amp;lt;i&amp;gt;β&amp;lt;/i&amp;gt;-Cell Mass, Insulin and Glucose Dynamics: Effect of Genetic Predisposition to Diabetes

Wiam Boutayeb,Mohamed Derouich,Mohamed E N Lamlili,Abdesslam Boutayeb

doi:10.4236/jbise.2014.76035

Abstract

Worldwide, diabetes is affecting 370 million people, causing nearly five million deaths and absorbing more than 471 billion USD per year. Mathematical models have been developed to simulate, analyse and understand the dynamics of β-cells, insulin and glucose. In this paper, we consider the effect of genetic predisposition to diabetes on dynamics of β-cells, glucose and insulin. We assume that the β-cell dynamics is governed by the differential equation: . The model indicates different behaviours according to the presence or absence of genetic predisposition. In presence of predisposition (ε = 1), the model shows three equilibrium points: a stable physiological equilibrium point (G = 100, I = 20, β = 600), a stable trivial pathological equilibrium point (G = 600, I = 0, β = 0) and a saddle point (G = 250, I = 9.8, β = 129.36). In absence of predisposition (ε = 0), the model has only two equilibrium points: an unstable pathological equilibrium point (G = 600, I = 0, β = 0) and a stable physiological equilibrium point (G = 82.6, I = 23, β = 900). In order to see how physical activity, obesity and other factors affect insulin sensitivity, simulations are carried out with different values of insulin induced glucose uptake rate (c), β-cell maximum insulin secretory rate (d) and environmental capacity (K).

Highlights

Once associated with economic development and considered as a disease of the rich, diabetes is affecting countries worldwide, threatening low and middle-income countries
Taking ε = 1 and using the values of parameters given in Table 1 yields results similar to those given by Topp, namely a physiological equilibrium point (G = 100, I = 20, β = 600), a trivial pathological equilibrium point (G = 600, I = 0, β = 0); and a saddle point (G = 250, I = 9.8, β = 129.36)
Assuming predisposition to diabetes (ε = 1), the qualitative behaviour of our model is similar to that of the models developed by Topp et al [12], Hernandez et al [13], and De Gaetano et al [14] represented by three equilibrium points: a stable physiological steady state; a trivial stable pathological severe diabetes steady state corresponding to a hyperglycaemic state with zero levels of β-cell mass and insulin, and an unstable saddle point with intermediate values of glycaemia, insulin and β-cell mass

Summary

Introduction

Once associated with economic development and considered as a disease of the rich, diabetes is affecting countries worldwide, threatening low and middle-income countries. Due to its chronic nature with severe complications, diabetes needs costly prolonged treatment and care, affecting individuals and societies, and raising the equity problem between and within countries [2]. Six of the top 10 countries with the highest prevalence of diabetes (in adults aged 20 to 79 years) are in this region: Kuwait (21.1%), Lebanon (20.2%), Qatar (20.2%), Saudi Arabia (20%), Bahrain (19.9%) and UAE (19.2%) [1] [3]. The direct and indirect socio-economic burden of diabetes is exponentially increasing in this region [4] [5]

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Discussion

Conclusion