The current COVID-19 pandemic is leading experts to assess the risks posed by the disease and compare policies geared towards stalling its evolution as a global pandemic. In this setting, the virus' basic reproductive number R _0, which characterizes the average number of secondary cases generated by each primary case, takes on a significant importance in the quantification of the potential scope of the pandemic . Yet, in most models, R _0 is assumed to be a universal constant for the virus across outbreak clusters and populations -- thus neglecting the inherent variability of the transmission process due to varying population densities, demographics, temporal factors, etc. In fact, it can be shown that the reproduction number is highly variable. Considering its expected value thus leads to biased or loose results in the reported predictive scenarios, especially as these are tailored to a given country or region. The goal of this paper is the examination of the impact of the reproductive number R's variability on important output metrics, and the percolation of this variability in projected scenarios so as to provide uncertainty quantification. In this perspective, instead of considering a single R_0, we consider a distribution of reproductive numbers R and devise a simple Bayesian hierarchical model that builds upon current methods for estimating the R to integrate its heterogeneity. We then simulate the spread of the epidemic , and the impact of different social distancing strategies using a probabilistic framework that models hospital occupancy. This shows 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 basic reproductive numbers, but rather to discuss 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 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.
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