The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from output measurements, its ability to yield correct insights – as well as the possibility of controlling the system – may be compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analysing and predicting the evolution of the COVID-19 pandemic. In this paper we survey the different models proposed in the literature, assembling a list of 36 model structures and assessing their ability to provide reliable information. We address the problem using the control theoretic concepts of structural identifiability and observability. Since some parameters can vary during the course of an epidemic, we consider both the constant and time-varying parameter assumptions. We analyse the structural identifiability and observability of all of the models, considering all plausible choices of outputs and time-varying parameters, which leads us to analyse 255 different model versions. We classify the models according to their structural identifiability and observability under the different assumptions and discuss the implications of the results. We also illustrate with an example several alternative ways of remedying the lack of observability of a model. Our analyses provide guidelines for choosing the most informative model for each purpose, taking into account the available knowledge and measurements.

最近的冠状病毒病 (COVID-19) 爆发极大地提高了公众对动态模型效用的认识和欣赏。与此同时，相互矛盾的模型预测的传播凸显了它们的局限性。如果模型的某些参数和/或状态变量无法从输出测量中确定，则其产生正确见解的能力以及控制系统的可能性可能会受到影响。流行病动力学通常使用隔间模型进行分析，并且此类模型的许多变体已用于分析和预测 COVID-19 大流行的演变。在本文中，我们调查了文献中提出的不同模型，汇总了 36 种模型结构的列表，并评估了它们提供可靠信息的能力。我们使用结构可识别性和可观察性的控制理论概念来解决这个问题。由于某些参数在流行病过程中可能会发生变化，因此我们同时考虑常数和时变参数假设。我们分析了所有模型的结构可识别性和可观察性，考虑了输出和时变参数的所有合理选择，这使我们分析了 255 个不同的模型版本。我们根据模型在不同假设下的结构可识别性和可观察性对模型进行分类，并讨论结果的含义。我们还通过示例说明了几种补救模型缺乏可观察性的替代方法。我们的分析提供了为每个目的选择信息最丰富的模型的指南，