Mathematical Modeling of The Effect of Epinephrine And Insulin On Blood Glucose Concentration

International Journal of Mathematics Trends and Technology (IJMTT)
© 2021 by IJMTT Journal
Volume-67 Issue-8
Year of Publication : 2021
Authors : K.W. Bunonyo, T.Y. Bunonyo


MLA Style: K.W. Bunonyo, T.Y. Bunonyo"Mathematical Modeling of The Effect of Epinephrine And Insulin On Blood Glucose Concentration" International Journal of Mathematics Trends and Technology 67.8 (2021):125-132. 

APA Style: K.W. Bunonyo, T.Y. Bunonyo(2021). Mathematical Modeling of The Effect of Epinephrine And Insulin On Blood Glucose Concentration  International Journal of Mathematics Trends and Technology, 67(8), 125-132.

In this research, we modeled the interaction between blood glucose and insulin, with epinephrine as treatment of diabetes. Diabetes is a syndrome of disordered metabolism, due to the combination of hereditary and environmental causes, resulting in abnormally high blood sugar levels. Different hormones in human body such as insulin, growth hormone, and glucagon control blood glucose concentration levels, epinephrine best known as adrenaline, glucocorticoids and thyroxin. The two most common forms of diabetes are due to either a diminished production of insulin (Type 1 diabetes), or diminished response by the body to insulin (Type 2 and gestational diabetes). Both lead to hyperglycemia, which largely causes the acute signs of diabetes: excessive urine production, resulting compensatory thirst and increased fluid intake, blurred vision, unexplained weight loss, lethargy, and changes in energy metabolism. The problem was modeled, solved and can be used to explain the dynamics of hormone, insulin is activation and how it affects glucose levels in blood. The results obtained are in line with those proposed by Hussian and Zadeng (2014), however, the previous researcher never considered constant supply of an epinephrine and other treatment, which give rise to the proposed models. The proposed models are in homogenous ordinary differential equations form, with the initial condition. In order to study the effect of insulin and epinephrine on the glucose concentration, we differentiated blood glucose concentration equation and substitute the insulin and epinephrine equations into the resulting equation from the glucose differentiation and simplified. The reduced nonlinear differential equation was solved using the method of variation of parameters where we obtained the particular solution. The numerical simulation was done using Mathematica, version 10 and the basic entry parameters were varied to study their effect on blood glucose concentration.


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Keywords : Modeling, Blood, Glucose, Concentration, Epinephrine, Diabetes