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Title: Computing the daily reproduction number of COVID-19 by inverting the renewal equation using a variational technique
Authors: Álvarez León, Luis Miguel 
Colom, Miguel
Morel, Jean-David
Morel, Jean-Michel
UNESCO Clasification: 120601 Construcción de algoritmos
3202 Epidemologia
Keywords: COVID-19
Renewal equation
Reproduction number
Integral equations
Issue Date: 2021
Journal: Proceedings of the National Academy of Sciences of the United States of America 
Abstract: The COVID-19 pandemic has undergone frequent and rapid changes in its local and global infection rates, driven by governmental measures, or the emergence of new viral variants. The reproduction number Rt indicates the average number of cases generated by an infected person at time t and is a key indicator of the spread of an epidemic. A timely estimation of Rt is a crucial tool to enable governmental organizations to adapt quickly to these changes and assess the consequences of their policies. The EpiEstim method is the most widely accepted method for estimating Rt. But it estimates Rt with a significant temporal delay. Here, we propose a new method, EpiInvert, that shows good agreement with EpiEstim, but that provides estimates of Rt several days in advance. We show that Rt can be estimated by inverting the renewal equation linking Rt with the observed incidence curve of new cases, it. Our signal processing approach to this problem yields both Rt and a restored it corrected for the “weekend effect” by applying a deconvolution + denoising procedure. The implementations of the EpiInvert and EpiEstim methods are fully open-source and can be run in real-time on every country in the world, and every US state through a web interface at
ISSN: 0027-8424
DOI: 10.1073/pnas.2105112118
Source: Proceedings of the National Academy of Sciences of the United States of America [ISSN 0027-8424], v. 118 (50), e2105112118, (Diciembre 2021)
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