A mechanistic and data-driven reconstruction of the time-varying reproduction number: Application to the COVID-19 epidemic
Authors: Cazelles Bernard , Champagne Clara , Nguyen-Van-Yen Benjamin , Comiskey Catherine , Vergu Elisabeta , Roche Benjamin 
Published: February 2021

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 by Bayesian inference (particle Markov Chain Monte Carlo method) 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. Except for the specific model structure, it is non-specifically assumed that the transmission rate follows a basic stochastic process constrained by the observations. This approach allows us to follow both the course of the COVID-19 epidemic and the temporal evolution of its Reff(t). Besides, it allows to assess and to interpret the evolution of transmission with respect to the mitigation strategies implemented to control the epidemic waves in France and in Ireland. We thus can estimate a reduction of more than 80% for the first wave in all the studied regions but a smaller reduction for the second wave when the epidemic was less active. For the third wave in Ireland the reduction was again significant (>70%).

Author Summary

In the early stages of any new epidemic, one of the first steps to design a control strategy is to estimate pathogen transmissibility in order to provide information on its potential to spread in the population. Among the different epidemiological indicators that characterize the transmissibility of a pathogen, the effective reproduction number Reff is commonly used for measuring time-varying transmissibility. It measures how many additional people can be infected by an infected individual during the course of an epidemic. However, Reff is difficult to estimate in the presence of silent transmission and/or significant temporal variation in case reporting. This is exactly the situation we are confronted with during this COVID-19 pandemic.

The statistical methods classically used for the estimation of Reff have some shortcomings in the rigorous consideration of the transmission characteristics of SARS-CoV-2. We propose here to use an original approach based on a stochastic model whose parameters vary in time and are inferred in a Bayesian framework from reliable hospital data. This enables us to reconstruct both the COVID-19 epidemic and its Reff. The Reff time evolution allows us to get information regarding the potential effects of mitigation measures taken during and between epidemics waves.

This approach, based on a stochastic model that realistically describes the hospital multiple datasets and which overcomes many of the biases associated with Reff estimates, appears to have some advantage over previously developed methods.