ANALYSIS OF THE MATHEMATICAL MODEL DESCRIBING THYROID-PITUITARY HORMONAL TRANSPORTATION BY A SYSTEM OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

Abstract

The main goal of this capstone project is to conduct the analysis of the mathematical model which describes the transportation of the thyroid pituitary axis of the hormones within the endocrine system. The model is constructed by a system of ordinary nonlinear differential equations that represent the fluctuations of the levels of the concentration of thyroxine hormone in the blood and illustrate its dependency on the concentration of certain enzymes. This capstone project will assess the stability of the system by applying the well-known Routh-Hurwitz criteria, conduct nu merical simulations, and use MATLAB with the purpose to visualize the general behaviour of the system. The derivation of the analytical solution separately for normal and degenerate states of the system is also presented in the paper. Lastly, the phenomena of relaxation oscillations that was noticed to take place during the derivation of the analytical solution will be explained. The research has shown that there is a direct correlation between the periodicity in the changes of the levels of thyroxine hormone in the blood and the presence of the symptoms of the schizophrenia. The current capstone project can be improved by modifying the model such that it includes the discrete and distributed delay cases during the trans portation process.