Stability Analysis for an Extended Model of the Hypothalamus-Pituitary-Thyroid Axis

We formulate and analyze a mathematical model
describing dynamics of the hypothalamus-pituitary-thyroid
homoeostatic mechanism in endocrine system. We introduce
to this system two types of couplings and delay. In our model,
feedback controls the secretion of thyroid hormones and delay
reflects time lags required for transportation of the hormones. The
influence of delayed feedback on the stability behaviour of the
system is discussed. Analytical results are illustrated by numerical
examples of the model dynamics. This system of equations describes
normal activity of the thyroid and also a couple of types of
malfunctions (e.g. hyperthyroidism).

Authors:

• Beata Jackowska-Zduniak

Keywords:

• Mathematical modeling
• ordinary differential equations
• endocrine system
• stability analysis.

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