Modeling the heterogeneity in COVID-19's reproductive number and its impact on predictive scenarios

The correct evaluation of the reproductive number $R$ for COVID-19 -- which characterizes the average number of secondary cases generated by each typical primary case -- is central in the quantification of the potential scope of the pandemic and the selection of an appropriate course of action. In most models, $R$ is modeled as a ``universal" constant for the virus across outbreak clusters and individuals -- effectively averaging the effect of the inherent variability of the transmission process due to varying population densities, demographics, temporal factors, etc. Yet, due to the exponential nature of epidemics growth, this simplification can lead to inaccurate predictions and/or risk evaluation, thus begging the question: how large is the impact of this simplification on predictions and risk estimates? How can this variability be percolated in the projections for the pandemics so as to provide a more accurate uncertainty quantification? In this perspective, instead of considering a single, fixed $R$, we model the reproductive number as a distribution sampled from a simple Bayesian hierarchical model. Using our fitted model, we then simulate the spread of the epidemic as well as the impact of different social distancing strategies, and highlight the strong impact of this added variability on the reported results. We emphasize that our goal is not to replace benchmark methods for estimating the reproductive numbers, nor to pretend to more accurate predictive scenarios. Rather, we focus solely on discussing the importance of the impact of $R$'s heterogeneity on uncertainty quantification for the current COVID-19 pandemic.