  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 out the inherent variability of the
transmission process due to varying individual contact rates, population
densities, demographics, or temporal factors amongst many. Yet, due to the
exponential nature of epidemic growth, the error due to this simplification can
be rapidly amplified and lead to inaccurate predictions and/or risk evaluation.
From the statistical modeling perspective, the magnitude of the impact of this
averaging remains an open question: how can this intrinsic variability be
percolated into epidemic models, and how can its impact on uncertainty
quantification and predictive scenarios be better quantified? In this paper, we
propose to study this question through a Bayesian perspective, creating a
bridge between the agent-based and compartmental approaches commonly used in
the literature. After deriving a Bayesian model that captures at scale the
heterogeneity of a population and environmental conditions, we 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 base our discussion on both synthetic experiments --
thereby quantifying of the reliability and the magnitude of the effects -- and
real COVID-19 data.
