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arXiv · 2012.02168

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

Marcos A. Capistrán·Antonio Capella·J. Andrés Christen
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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.

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Marcos A. Capistrán, Antonio Capella, J. Andrés Christen. 2020-12-03. Filtering and improved Uncertainty Quantification in the dynamic estimation of effective reproduction numbers. https://arxiv.org/abs/2012.02168

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