Mathematical models are a powerful tool when used to describe ectotherms' life cycles, above all for their suitability in being utilised for decision support systems. In particular, two models continue to arouse the interest of the scientific community and inspire new developments: the Manetsch-VanSickle Distributed Delay Model and the Von Foerster equation. Even though these models have been widely studied, discussed and applied, some aspects relating to their different points of view in representations of the same life cycle are yet to be explored. One of the main issues open for ongoing investigation is the different modes of division in preimaginal stages, which leads to different interpretations of the concept of age between the two models. The Distributed Delay Model considers a subdivision in h chained preimaginal stages with the same size, based on the concept of physiological time, in which the development of the species is related to the daily average temperature. On the other hand, the Von Foerster equation considers chronological age, defined commonly as a time with a different scale.

This work highlights the analogies between the two models and shows, using the case study of L. botrana, how to obtain the number of the h stages considered by the Distributed Delay Model, from the number of observed preimaginal stages of the Von Foerster equation. To make the models comparable, the upwind scheme has been applied to the Von Foerster equation, leading to a system of ordinary differential equations that is similar to the Distributed Delay Model.

数学模型在描述等温线的生命周期时是一个强大的工具，首先是因为它们适用于决策支持系统。特别是，两个模型继续引起科学界的兴趣并激发新的发展：Manetsch-VanSickle分布式延迟模型和Von Foerster方程。尽管已经对这些模型进行了广泛的研究，讨论和应用，但在相同生命周期表示中，与它们的不同观点相关的某些方面仍待探索。正在进行研究的主要问题之一是在想象前阶段的划分方式不同，这导致了两种模型之间对年龄概念的不同解释。分布式延迟模型考虑了h的细分基于生理时间的​​概念，大小相同的链状成象前阶段，其中物种的发育与每日平均温度有关。另一方面，冯·福斯特（Von Foerster）方程考虑的是年代年龄，通常将其定义为不同比例的时间。

这项工作着重说明了两个模型之间的类比，并通过使用博特兰乳杆菌的案例研究，展示了如何从观察到的冯·福斯特方程的想象中级数中获得由分布延迟模型考虑的h级数。为了使模型具有可比性，已将逆风方案应用于Von Foerster方程，从而形成了一个与分布延迟模型相似的常微分方程组。