Theses and Dissertations

Date of Award


Document Type


Degree Name

Master of Science (MS)



First Advisor

Dr. Vesselin Vatchev

Second Advisor

Dr. Andras Balogh

Third Advisor

Dr. Dambaru Bhatta


We study a mathematical modeling of nonlinear dynamics of blood hormones, which includes glucose and insulin. On Chapter I, II, III and IV, we introduce this work, analyze an effect of the secreted insulin by the pancreatic beta cells and glucagon hormones and state concluding remarks, respectively. This model considers the time evolution of nonlinear dynamics of the equations for glucose, glucagon and insulin concentrations plus insulin and glucagon actions and the secreted insulin as a result of elevation of glucose in the blood plasma. Using both analytical and numerical procedures, we determine such quantities using different parameters for different individuals and at different times of the day. We find that the nonlinear effects between these hormones can be notable and affect the resulting values for each hormone for given instant in time. We find that smaller parameters can lead to moderate or smaller values of the glucose plasma concentration.


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