Modeling the Heterogeneity in COVID-19's Reproductive Number and Its Impact on Predictive Scenarios

The correct evaluation of the reproductive number for COVID-19 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 constant - effectively averaging out the inherent variability of the transmission process due to varying individual contact rates, population densities, 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 its extent remains unknown. How can this intrinsic variability be percolated into epidemic models, and its impact, better quantified? We study this question here through a Bayesian perspective that captures at scale the heterogeneity of a population and environmental conditions, creating a bridge between the traditional agent-based and compartmental approaches. We use our model to simulate the spread as well as the impact of different social distancing strategies on real COVID-19 data, and highlight the significant impact of the heterogeneity. We emphasize that the contribution of this paper focuses on discussing the importance of the impact of R's heterogeneity on uncertainty quantification from a statistical viewpoint, rather than developing new predictive models.