Intrinsic randomness in epidemic modelling beyond statistical uncertainty

Abstract Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority frameworks assessing infectious disease risk consider only uncertainty. We ever observe a single epidemic, and therefore cannot empirically determine Here, we characterise both uncertainty using time-varying general branching process. Our framework explicitly decomposes variance into mechanistic components, quantifying the contribution to produced by each factor in epidemic process, how these contributions vary over time. an outbreak is itself renewal equation where past affects future variance. find that, superspreading not necessary for substantial uncertainty, profound variation size occur even without overdispersion offspring distribution (i.e. number secondary infections infected person produces). Aleatoric forecasting grows dynamically rapidly, so significant underestimate. Therefore, failure account will ensure that policymakers are misled about substantially higher true extent potential risk. demonstrate our method, which underestimated, two historical examples.