Mathematical Modelling and Simulation of <i>β</i>-Cell Mass, Insulin and Glucose Dynamics: Effect of Genetic Predisposition to Diabetes

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 ).