ANALYSIS OF THE MATHEMATICAL MODEL DESCRIBING THYROID-PITUITARY HORMONAL TRANSPORTATION BY A SYSTEM OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS
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Date
2022-05
Authors
Baidildayeva, Aisha
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Sciences and Humanities
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.
Description
Keywords
Type of access: Open Access, endocrine system
Citation
Aisha Baidildayeva. 2022. Analysis of the mathematical model describing thyroid-pituitary hormonal transportation by a system of nonlinear ordinary differential equations. School of Sciences and Humanities