Solution of a Mathematical Model Describing the Change of Hormone Level in Thyroid Using the Laplace Transform

Abstract

In the present paper, a mathematical model describing the thyroid-pituitary homeostatic mechanism is analyzed for its physiological and clinical significance. The influence of different parameters on the stability behavior of the system is discussed. We have assumed in the present paper that the rate of thyrotropin production is reduced by an amount which is proportional to the blood concentration of thyroxine and also the rate of loss of thyrotropin is proportional to the existing thyrotropin concentration. The stability behavior of the system is analyzed and the possibility of occurrence of periodic solutions is looked into. As the pituitary gland can produce no output in the presence of thyroxine concentration greater than a certain value, we have also included a degenerate form of the equation for thyrotropin production in the present paper. The solutions of the system of governing equations are obtained by applying the Laplace transform. Also, the nature of the solution is interpreted graphically using the Maple12 technique for both stable and unstable behavior.