A Stochastic Biomathematical Model of the Male Reproductive Hormone System

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Abstract
A stochastic biomathematical model for the male reproductive hormone system (gonadotropin-releasing hormone, luteinizing hormone, and testosterone) is developed. Hormone secretion occurs as either a continuous release, a pulsatile release, or a combination thereof; in the latter two, hormone molecules are stored and later released. Each form of release is represented within the male system. The model begins at the cellular level of hormone synthesis, aggrandizes to the level of the gland and secretion, and finally to the level of elimination and circulation in the blood. The model consists of a system of stochastic integrodifferential equations which describe the nonlinear time-delayed feedback from concentrations (of the various hormones) on their rates of hormone synthesis. A stochastic formulation is established, showing that the various imposed structures are consistent with one another. Computer experiments are performed and compared to analogous clinical experiments (where components are decoupled via pharmacological intervention) to show the dynamic range of the model and its potential usefulness (e.g., assessing the pathway of the circadian rhythm).

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