Strathprints Home | Open Access | Browse | Search | User area | Copyright | Help | Library Home | SUPrimo

A delay differential equation mathematical model for the control of the hormonal system of the hypothalamus, the pituitary and the testis in man

Greenhalgh, David and Khan, Qamar (2010) A delay differential equation mathematical model for the control of the hormonal system of the hypothalamus, the pituitary and the testis in man. In: Workshop on multiscale modelling of biological systems, 2010-07-05 - 2010-07-06, Stirling.

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

In this paper we develop previously studied mathematical models of the regulation of testosterone by luteinizing hormone and luteinizing hormone release hormone in the human body. We propose a delay differential equation mathematical model which improves on earlier simpler models by taking into account observed experimental facts. We show that our model has four possible equilibria, but only one unique equilibrium where all three hormones are present. We perform stability and Hopf bifurcation analyses on the equilibrium where all three hormones are present. With no time delay this equilibrium is unstable, but as the time delay increases through an infinite sequence of positive values Hopf bifurcation occurs repeatedly. This is of practical interest as biological evidence shows that the levels of these hormones in the body oscillate periodically. We next discuss stability of the other equilibria heuristically using analytical methods. Then we describe simulations with realistic parameter values and show that our model can mimic the regular fluctuations of the three hormones in the body and explore numerically some of our heuristic conjectures. A brief discussion concludes the paper.

Item type: Conference or Workshop Item (Other)
ID code: 41305
Keywords: human hormonal systems, testosterone, luteinizing hormone, luteinizing hormone release hormone, time delay, differential equations, equilibrium and stability, limit cycles, Hopf bifurcation, Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
Depositing user: Pure Administrator
Date Deposited: 01 Oct 2012 15:05
Last modified: 04 Oct 2012 17:59
URI: http://strathprints.strath.ac.uk/id/eprint/41305

Actions (login required)

View Item