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 .
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 .
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the effect of the
out the
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individual contact rates,
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temporal factors, etc
or temporal factors amongst many
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epidemics growth,
epidemic growth, the error due to
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be rapidly amplified and
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, thus begging the question: how large is
. From the statistical modeling perspective,
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magnitude of the
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simplification on predictions and risk estimates? How can this
averaging remains an open question: how can this intrinsic
R
in the projections for the pandemics so as to provide a more accurate uncertainty quantification
into epidemic models, and how can its impact on uncertainty quantification and predictive scenarios be better quantified
R
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
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
R
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
base our discussion on both synthetic experiments -- thereby quantifying of the reliability and the magnitude of the effects -- and real
R
pandemic
data