A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic

Cazelles, B.; Champagne, C.; Nguyen Van Yen, B.; Comiskey, C.; Vergu, E.; Roche, B.

The effective reproduction number Reff is a critical epidemiological parameter that characterizes the transmissibility of a pathogen. However, this parameter is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This variation can occur due to the lack of timely or appropriate testing, public health interventions and/or changes in human behavior during an epidemic. This is exactly the situation we are confronted with during this COVID-19 pandemic. In this work, we propose to estimate Reff for the SARS-CoV-2 (the etiological agent of the COVID-19), based on a model of its propagation considering a time-varying transmission rate. This rate is modeled by a Brownian diffusion process embedded in a stochastic model. The model is then fitted with Bayesian inference (PMCMC) using multiple well-documented hospital datasets from several regions in France and in Ireland. This mechanistic modeling framework enables us to reconstruct the temporal evolution of the transmission rate of the COVID-19 based only on the available data, without any specific hypothesis on its evolution. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its Reff(t). In this way, we can appropriately assess the effect of the mitigation strategies implemented to control the epidemic waves in France and in Ireland.