Intrinsic Randomness in Epidemic Modelling Beyond Statistical Uncertainty

TL;DR

This paper introduces a framework to distinguish and quantify intrinsic (aleatoric) and knowledge-based (epistemic) uncertainties in epidemic modeling, revealing that intrinsic randomness significantly impacts outbreak size predictions.

Contribution

It develops a novel decomposition method for aleatoric uncertainty in epidemic processes, highlighting its importance beyond overdispersion and superspreading.

Findings

Aleatoric uncertainty can cause large outbreak variability without superspreading.

Forecasting with only epistemic uncertainty underestimates true risk.

Intrinsic randomness grows rapidly, affecting epidemic predictions over time.

Abstract

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.