Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas 79409-1042, United States.
Math Biosci Eng. 2014 Jun;11(3):403-25. doi: 10.3934/mbe.2014.11.403.
Stochastic versions of several discrete-delay and continuous-delay differential equations, useful in mathematical biology, are derived from basic principles carefully taking into account the demographic, environmental, or physiological randomness in the dynamic processes. In particular, stochastic delay differential equation (SDDE) models are derived and studied for Nicholson's blowflies equation, Hutchinson's equation, an SIS epidemic model with delay, bacteria/phage dynamics, and glucose/insulin levels. Computational methods for approximating the SDDE models are described. Comparisons between computational solutions of the SDDEs and independently formulated Monte Carlo calculations support the accuracy of the derivations and of the computational methods.
从基本原理出发，通过仔细考虑动态过程中的人口统计学、环境或生理学随机性，推导出了几种离散时滞和连续时滞微分方程的随机版本，这些方程在数学生物学中非常有用。特别是，针对尼科尔斯ons 蝇方程、哈钦森方程、具有时滞的 SIS 传染病模型、细菌/噬菌体动力学和葡萄糖/胰岛素水平，推导出并研究了随机时滞微分方程（SDDE）模型。还描述了用于近似 SDDE 模型的计算方法。SDDE 的计算解与独立制定的蒙特卡罗计算之间的比较支持了推导和计算方法的准确性。
