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A Mathematical Model on Glucose Homeostasis in Type 1 Diabetes

In: Disease Prevention and Health Promotion in Developing Countries

Author

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  • Wiam Boutayeb

    (School of High Studies in Engineering)

Abstract

The aim of this chapter is to propose a mathematical model describing the interaction between Insulin, Glucose and Free Fatty Acids (FFA) while considering injected insulin bolus ($$I_0$$I0) in a type 1 diabetes person. The proposed mathematical model is governed by three ordinary differential equations representing respectively: The dynamics of insulin in which subcutaneous bolus injection ($$I_0$$I0) is introduced. The dynamics of glucose in which glucose production by liver and kidney and glucose from carbohydrate intake are separated. The dynamics of FFA. Stability analysis shows that the ordinary differential system has one positive equilibrium point ($$I^*, G^*, F^*$$I∗,G∗,F∗). Using numerical parameter values, the equilibrium is shown to be locally stable. Simulation was carried out for different values of the parameters, in particular according to variation in carbohydrate intake ($$a_2$$a2), insulin sensitivity (c) and the insulin bolus injected ($$I_0$$I0). The model shows clearly that a disorder in injected insulin, carbohydrate intake or physical activity may lead to dangerous situations of chronic hyperglycemia leading with time, to diabetes complications or hypoglycemia that may also lead to loss of consciousness or even to a sudden death.

Suggested Citation

  • Wiam Boutayeb, 2020. "A Mathematical Model on Glucose Homeostasis in Type 1 Diabetes," Springer Books, in: Abdesslam Boutayeb (ed.), Disease Prevention and Health Promotion in Developing Countries, chapter 0, pages 251-258, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-34702-4_15
    DOI: 10.1007/978-3-030-34702-4_15
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