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

The effective reproduction number Rt 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 Rt, as expected by the observed variability in contagion patterns. We elaborate on the Bayesian estimation of Rt 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 Rts, 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 Rt'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.