标题： 延迟在生物系统延迟随机模拟中的解释 显示英文标题

标题： On the Interpretation of Delays in Delay Stochastic Simulation of Biological Systems

摘要： 生物系统中的延迟可用于模拟那些底层动态无法精确观察到的事件。 具有延迟的生物系统的数学建模通常基于延迟微分方程（DDEs），这是一种微分方程，其中未知函数在某一时间的导数是根据该函数在之前时间的值来给出的。 在文献中，已经提出了延迟随机模拟算法。 这些算法采用“延迟作为持续时间”的方法，即它们基于将延迟解释为化学反应开始和终止之间经过的时间。 这种解释不适合某些类型的生物系统，在这些系统中，参与延迟相互作用的物种可能同时参与其他相互作用。 我们通过一个肿瘤生长的DDE模型展示了用于随机模拟的“延迟作为持续时间”的方法并不准确，并提出了一种基于“纯粹延迟”解释的模拟算法，该算法在所考虑的模型上提供了更好的结果。 显示英文摘要

摘要： Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed. Mathematical modeling of biological systems with delays is usually based on Delay Differential Equations (DDEs), a kind of differential equations in which the derivative of the unknown function at a certain time is given in terms of the values of the function at previous times. In the literature, delay stochastic simulation algorithms have been proposed. These algorithms follow a "delay as duration" approach, namely they are based on an interpretation of a delay as the elapsing time between the start and the termination of a chemical reaction. This interpretation is not suitable for some classes of biological systems in which species involved in a delayed interaction can be involved at the same time in other interactions. We show on a DDE model of tumor growth that the delay as duration approach for stochastic simulation is not precise, and we propose a simulation algorithm based on a ``purely delayed'' interpretation of delays which provides better results on the considered model.