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Mathematical Medicine and Biology 2005 22(1):15-33; doi:10.1093/imammb/dqh020
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© The Author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. For Permissions, please email: journals.permissions@oupjournals.org

A delay-differential equation model of the feedback-controlled hypothalamus–pituitary–adrenal axis in humans

Yongwimon Lenbury * and Pornsarp Pornsawad

Department of Mathematics, Faculty of Science, Mahidol University, Rama 6 Rd., Bangkok 10400, Thailand

The present work develops and analyses a model system of delay-differential equations which describes the core dynamics of the stress-responsive hypothalamus–pituitary–adrenal axis. This neuroendocrine ensemble exhibits prominent pulsatile secretory patterns governed by nonlinear and time-delayed feedforward and feedback signal interchanges. Formulation and subsequent bifurcation analysis of the model provide a qualitative and mathematical frame work for a better understanding of the delayed responsive mechanisms as well as the dynamic variations in different pathological situations.

Keywords: cortisol secretion; delay-feedback controlled system; Hopf bifurcation; nonlinear model

* Corresponding author.


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