Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, UK.
Phytopathology. 2012 Apr;102(4):365-80. doi: 10.1094/PHYTO-12-10-0338.
Compartmental models have become the dominant theoretical paradigm in mechanistic modeling of plant disease and offer well-known advantages in terms of analytic tractability, ease of simulation, and extensibility. However, underlying assumptions of constant rates of infection and of exponentially distributed latent and infectious periods are difficult to justify. Although alternative approaches, including van der Plank's seminal discrete time model and models based on the integro-differential formulation of Kermack and McKendrick's model, have been suggested for plant disease and relax these unrealistic assumptions, they are challenging to implement and to analyze. Here, we propose an extension to the susceptible, exposed, infected, and removed (SEIR) compartmental model, splitting the latent and infection compartments and thereby allowing time-varying infection rates and more realistic distributions of latent and infectious periods to be represented. Although the model is, in fact, more general, we specifically target plant disease by demonstrating how it can represent both the van der Plank model and the most commonly used variant of the Kermack and McKendrick (K & M) model (in which the infectivity response is delay Gamma distributed). We show how our reformulation retains the numeric and analytic tractability of SEIR models, and how it can be used to replicate earlier analyses of the van der Plank and K & M models. Our reformulation has the advantage of using elementary mathematical techniques, making implementation easier for the nonspecialist. We show a practical implication of these results for disease control. By taking advantage of the easy extensibility characteristic of compartmental models, we also investigate the effects of including additional biological realism. As an example, we show how the more realistic infection responses we consider interact with host demography and lead to divergent invasion thresholds when compared with the "standard" SEIR model. An ever-increasing number of analyses purportedly extract more biologically realistic invasion thresholds by adding additional biological detail to the SEIR model framework; we contend that our results demonstrate that extending a model that has such a simplistic representation of the infection dynamics may not, in fact, lead to more accurate results. Therefore, we suggest that modelers should carefully consider the underlying assumptions of the simplest compartmental models in their future work.
房室模型已成为植物病害机械建模的主要理论范例，在分析的可处理性、模拟的简易性和可扩展性方面具有明显的优势。然而，感染率恒定和潜伏和传染期呈指数分布的基本假设很难证明。尽管已经提出了替代方法，包括范德普兰克开创性的离散时间模型和基于 Kermack 和 McKendrick 模型的积分微分公式的模型，用于放松这些不现实的假设，但它们实施和分析具有挑战性。在这里，我们提出了对易感、暴露、感染和消除（SEIR）房室模型的扩展，将潜伏和感染隔室分开，从而可以表示时变的感染率和更现实的潜伏和传染期分布。虽然该模型实际上更为通用，但我们通过展示它如何代表范德普兰克模型和最常用的 Kermack 和 McKendrick（K&M）模型变体（其中感染性响应呈延迟伽马分布），专门针对植物病害。我们展示了我们的重新表述如何保留 SEIR 模型的数值和可分析性，以及如何用于复制范德普兰克和 K&M 模型的早期分析。我们的重新表述具有使用基本数学技术的优势，使非专业人员更容易实现。我们展示了这些结果对疾病控制的实际影响。通过利用房室模型易于扩展的特点，我们还研究了包含额外生物学现实性的影响。作为一个例子，我们展示了我们考虑的更现实的感染反应如何与宿主种群动态相互作用，并与“标准”SEIR 模型相比导致不同的入侵阈值。越来越多的分析声称通过向 SEIR 模型框架添加额外的生物学细节来提取更具生物学现实性的入侵阈值；我们认为，我们的结果表明，扩展一个对感染动力学具有如此简单表示的模型实际上可能不会导致更准确的结果。因此，我们建议建模者在未来的工作中仔细考虑最简单房室模型的基本假设。
