Assessing bias in susceptible-infected-recovered estimation from aggregated epidemic data

The canonical susceptible-infected-recovered (SIR) epidemic model is ubiquitous in assessing severity to guide interventions. It is typically applied to hierarchically aggregated data from distinct sub-regions. The introduced heterogeneity can lead to significant errors in estimated epidemic severity. We develop three analytical methods to extract SIR parameters from data, focusing on the reproduction number $R_0$ that quantifies epidemic wave severity/strength. The estimation methods are applied to synthetically aggregated incidence data formulated by summing two independent SIR solutions of distinct $R_0$ and separated by an onset delay, i.e. temporal offset. When applying the SIR model, we find that $R_0$ estimates from the aggregated data can underestimate or overestimate the constituent epidemic waves' $R_0$ even when the prediction appears to agree well with the incidence data, resulting in an erroneous unimodal epidemic dynamics. We find that for two epidemic waves, the stronger the trailing wave, the longer the temporal offset that maintains apparent erroneous unimodal aggregated data. In the special case of two equivalent epidemic strengths, however, the weaker the waves, the longer the offset that maintains apparent unimodal aggregated data. We provide sensitivity analyses with respect to noise perturbation of the data and illustrate our approach using historical influenza data.