Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). Majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever observe a single epidemic, and therefore cannot empirically determine aleatoric uncertainty. Here, for the first time, we characterise both epistemic and aleatoric uncertainty using a time-varying general branching processes. Our framework explicitly decomposes aleatoric variance into mechanistic components, quantifying the contribution to uncertainty produced by each factor in the epidemic process, and how these contributions vary over time. The aleatoric variance of an outbreak is itself a renewal equation where past variance affects future variance. Surprisingly, superspreading is not necessary for substantial uncertainty, and profound variation in outbreak size can occur even without overdispersion in the distribution of the number of secondary infections. Aleatoric forecasting uncertainty grows dynamically and rapidly, and so forecasting using only epistemic uncertainty is a significant underestimate. Failure to account for aleatoric uncertainty will ensure that policymakers are misled about the substantially higher true extent of potential risk. We demonstrate our method, and the extent to which potential risk is underestimated, using two historical examples: the 2003 Hong Kong severe acute respiratory syndrome (SARS) outbreak, and the early 2020 UK COVID-19 epidemic. Our framework provides analytical tools to estimate epidemic uncertainty with limited data, to provide reasonable worst-case scenarios and assess both epistemic and aleatoric uncertainty in forecasting, and to retrospectively assess an epidemic and thereby provide a baseline risk estimate for future outbreaks. Our work strongly supports the precautionary principle in pandemic response.
翻译:不确定性可以被归类为不透明性(不自然的随机性)或癫痫性(对参数的了解不准确)。评估传染病风险的框架大多只考虑传染性不确定性。我们只观察到单一的流行病,因此无法以经验方式确定消散性不确定性。在这里,我们首次使用时间变化的一般分流进程,将癫痫和感缓性不确定性定性为隐性成分,明确分解为机能性成分,量化流行病过程中每个因素造成的不确定性,以及这些不确定性随时间变化的不同而变化。 传染病风险本身的偏缓性差异是一个更新的方程,而过去的差异影响未来差异。 令人惊讶的是,对于巨大的不确定性来说,超大爆发规模的波动是必要的,即使没有在二次感染的分布中出现过度的偏差,也有可能发生。 诊断性预测性不确定性以动态和快速的速度增长,因此仅使用流行性不确定性的预测是一种显著的低估。 不计分解性不确定性,因此,对于流行病的预测性不确定性本身是一个更新的方形变异性变化,因此,对2003年期变变变本法的深度的不确定性和潜在风险将证明:在2003年中,我们的方法将产生深刻的精确性分析,而使真正的变本变本。