IDENTIFIABILITY OF INFECTION MODEL PARAMETERS EARLY IN AN EPIDEMIC
IDENTIFIABILITY OF INFECTION MODEL PARAMETERS EARLY IN AN EPIDEMIC
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DOI：
10.1137/20m1353289
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发表时间：
2022-01-01
影响因子：
2.2
通讯作者：
Schiff, Steven J.
中科院分区：
文献类型：
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作者：
Sauer, Timothy;Berry, Tyrus;Schiff, Steven J.
已知确定性和随机SEIR流行病模型中的参数在结构上是可识别的。例如，根据对整个疫情期间感染人群时间序列I(t)的了解，可以成功地估计参数。在本文中，我们观察到，如果只有流行病早期（高峰前）的感染病例数据，估计将在实践中失败。这个事实可以用众所周知的动态补偿现象来解释。我们使用这一概念在SEIR参数空间中推导出一个不可识别流形，该流形由流行病早期与I(t)不可区分的参数组成。因此，可识别性取决于可用于观察的系统轨迹的范围。虽然不可识别流形的存在阻碍了准确确定参数的能力，但我们认为它可能对不确定度量化有用。本文还分析了最近提出的一种用于COVID-19建模的SEIR变体，并推导了类似的不可识别曲面。
It is known that the parameters in the deterministic and stochastic SEIR epidemic models are structurally identifiable. For example, from knowledge of the infected population time series I(t) during the entire epidemic, the parameters can be successfully estimated. In this article we observe that estimation will fail in practice if only infected case data during the early part of the epidemic (prepeak) is available. This fact can be explained using a well-known phenomenon called dynamical compensation. We use this concept to derive an unidentifiability manifold in the parameter space of SEIR that consists of parameters indistinguishable from I(t) early in the epidemic. Thus, identifiability depends on the extent of the system trajectory that is available for observation. Although the existence of the unidentifiability manifold obstructs the ability to exactly determine the parameters, we suggest that it may be useful for uncertainty quantification purposes. A variant of SEIR recently proposed for COVID-19 modeling is also analyzed, and an analogous unidentifiability surface is derived.