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The effective reproduction number $R_t$ measures an infectious disease'stransmissibility as the number of secondary infections in one reproduction timein a population having both susceptible and non-susceptible hosts. Currentapproaches do not quantify the uncertainty correctly in estimating $R_t$, asexpected by the observed variability in contagion patterns. We elaborate on theBayesian estimation of $R_t$ by improving on the Poisson sampling model of Coriet al. (2013). By adding an autoregressive latent process, we build a DynamicLinear Model on the log of observed $R_t$s, resulting in a filtering typeBayesian inference. We use a conjugate analysis, and all calculations areexplicit. Results show an improved uncertainty quantification on the estimationof $R_t$'s, with a reliable method that could safely be used by non-experts andwithin other forecasting systems. We illustrate our approach with recent datafrom the current COVID19 epidemic in Mexico.

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