Filtering and improved Uncertainty Quantification in the dynamic estimation of effective reproduction numbers

TL;DR

This paper improves the Bayesian estimation of the effective reproduction number in infectious diseases by incorporating an autoregressive process, leading to better uncertainty quantification and practical applicability in epidemic monitoring.

Contribution

It introduces a novel filtering-based Bayesian method with an autoregressive component for more accurate $R_t$ uncertainty estimation, enhancing existing models.

Findings

Enhanced uncertainty quantification in $R_t$ estimates.

Explicit calculations using conjugate analysis.

Application to COVID-19 data in Mexico.

Abstract

The effective reproduction number $R_t$ measures an infectious disease's transmissibility as the number of secondary infections in one reproduction time in a population having both susceptible and non-susceptible hosts. Current approaches do not quantify the uncertainty correctly in estimating $R_t$, as expected by the observed variability in contagion patterns. We elaborate on the Bayesian estimation of $R_t$ by improving on the Poisson sampling model of Cori et al. (2013). By adding an autoregressive latent process, we build a Dynamic Linear Model on the log of observed $R_t$s, resulting in a filtering type Bayesian inference. We use a conjugate analysis, and all calculations are explicit. Results show an improved uncertainty quantification on the estimation of $R_t$'s, with a reliable method that could safely be used by non-experts and within other forecasting systems. We illustrate our approach with recent data from the current COVID19 epidemic in Mexico.