A mathematical model for type 1 diabetes, on the effect of growth hormone

Abstract

Diabetes mellitus is a metabolic disorder characterized by chronic hyperglycemia with disturbances of carbohydrate, fat and protein metabolism resulting from defect in insulin secretion, insulin action, or both. The three main types of diabetes are: type 1 diabetes, type 2 diabetes and gestational diabetes. As it is associated to a deficient insulin production, type 1 diabetes requires daily administration of insulin accompanied with a strict continuous control of carbohydrate intake in order to ensure a diabetes-free glycemic level. In this paper, a mathematical model governed by ordinary differential equations is presented to describe interaction between insulin, glucose, free fatty acids and growth hormone in the case of type 1 diabetes. Stability analysis is carried out and the dynamics of glucose is illustrated by a simulation using different parameter values.