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

Greenhalgh, D. and Khan, Q.J.A. and , Sultan Qaboos University, Oman (Funder) (2009) A delay differential equation mathematical model for the control of the hormonal system of the hypothalamus, the pituitary and the testis in man. Nonlinear Analysis: Theory, Methods and Applications, 71 (12). e925-e935. ISSN 0362-546X

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    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: Article
    ID code: 14027
    Keywords: human hormonal systems, testosterone, luteinizing hormone, luteinizing hormone release hormone, time delay, differential equations, equilibrium and stability analysis, limit cycles, Hopf bifurcation, Mathematics, Biology, Analysis, Applied Mathematics
    Subjects: Science > Mathematics
    Science > Natural history > Biology
    Department: Faculty of Science > Mathematics and Statistics
    Related URLs:
      Depositing user: Mrs Ann Lynch
      Date Deposited: 08 Dec 2009 09:50
      Last modified: 05 Sep 2014 23:38
      URI: http://strathprints.strath.ac.uk/id/eprint/14027

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