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

Abstract

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 can thus 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, around 45% in France but just 20% in Ireland. For the third wave in Ireland the reduction was again significant (>70%).

Dynamic parameterization of a modified SEIRD model to analyze and forecast the dynamics of COVID-19 outbreaks in the United States

“…Additionally, our computational pipeline could be recast in a Bayesian framework to accommodate a more robust quantification of uncertainty from the input data to model forecasting [18,35]. With these developments, the computational pipeline could also palliate large oscillations in the daily parameter estimates between successive calibrations, and hence yield more reliable forecasts.…”

“…Hybrid approaches have been developed to overcome the limitations of the classic statistical and mechanistic modeling paradigms [33]. By using data-driven dynamic parameterizations of mechanistic models and leveraging techniques borrowed from statistical approaches, hybrid models have shown an improvement over purely statistical or mechanistic models in terms of explaining the changing nature of mechanistic parameters due to human behavior and government interventions [31,34,35]. To calibrate and update time-resolved parameterizations of mechanistic models using incoming epidemiological data, some studies have shown promising results by leveraging Bayesian methods [36,37].…”

Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise

“…In [44], a direct stochastic model is proposed for R t , assuming that its log derivative is Brownian, namely…”

Dynamics of the COVID-19 epidemic in Ireland under mitigation

“…An interesting sub-product of our framework is the possibility of estimating the time evolution of the effective reproduction number, R eff [12]. R eff is defined as the mean number of infections generated during the infectious period of a single infectious case at time t. It can be easily estimated using the steady-state form of a SEIR model.…”