France J, Thornley J H, Dhanoa M S, Siddons R C
J Theor Biol. 1985 Apr 21;113(4):743-58. doi: 10.1016/s0022-5193(85)80191-0.
A unifying mathematical analysis of the use of compartmental models with and without time lags is given, with particular reference to the use of such models for digesta movement along the gastro-intestinal tract of the ruminant. First the generalized compartmental model without time lags is developed, and then it is shown how discrete time lags may be incorporated into this formalism. The important relationship between distributed lags, especially the gamma-distributed time lags, and the equivalent compartmental scheme, is emphasized. It is shown how distributed time lags can be included in a general compartmental model. The treatment covers, as special cases, some widely used models, and shows their relationship to each other and to other possible models. Finally a compartmental interpretation is outlined for a recently proposed double-exponential model.
本文给出了对带有时滞和不包含时滞的房室模型应用的统一数学分析，特别提及此类模型在反刍动物胃肠道中食糜移动方面的应用。首先推导了不包含时滞的广义房室模型，然后展示了如何将离散时滞纳入该形式体系。强调了分布时滞（特别是伽马分布时滞）与等效房室方案之间的重要关系。展示了如何将分布时滞纳入一般房室模型。作为特殊情况，该论述涵盖了一些广泛使用的模型，并展示了它们彼此之间以及与其他可能模型的关系。最后概述了对最近提出的双指数模型的房室解释。
