Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The 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, we characterise both epistemic and aleatoric uncertainty using a time-varying general branching process. 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. We find that, superspreading is not necessary for substantial uncertainty, and profound variation in outbreak size can occur even without overdispersion in the offspring distribution (i.e. the distribution of the number of secondary infections an infected person produces). Aleatoric forecasting uncertainty grows dynamically and rapidly, and so forecasting using only epistemic uncertainty is a significant underestimate. Therefore, 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.

翻译：不确定性可分为偶然性（内在随机性）与认知性（参数知识不完备）。大多数传染病风险评估框架仅考虑认知不确定性。我们每次只能观测到单次疫情，因此无法通过经验确定偶然性不确定性。本研究利用时变一般分支过程表征认知与偶然两种不确定性。该框架将偶然性方差显式分解为机制性成分，量化疫情过程中各因素对不确定性的贡献及其随时间的变化。疫情的偶然性方差本身构成一个更新方程，其中过往方差影响未来方差。研究发现：极端不确定性并不必然需要超级传播事件的发生，即使在后代分布（即感染者产生的续发病例数分布）不存在过度离散的情况下，疫情规模仍可能出现剧烈变异。偶然性预测不确定性呈动态快速增长态势，因此仅基于认知不确定性的预测将导致显著低估。若忽视偶然性不确定性，决策者将无法获知潜在风险的实际严重程度。我们通过两个历史案例演示了该方法及潜在风险被低估的程度。