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Article

Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise

1
Departamento de Informática y Sistemas, Universidad de Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain
2
Laboratory of Integrative Systems Physiology, Ecole Polytechnique Fédérale de Lausanne, EPFL/IBI/LISP—Station 15, CH-1015 Lausanne, Switzerland
3
ENS Paris-Saclay, CNRS, Centre Borelli, Université Paris-Saclay, F-91190 Gif-sur-Yvette, France
*
Author to whom correspondence should be addressed.
Academic Editors: Jacques Demongeot and Pierre Magal
Biology 2022, 11(4), 540; https://doi.org/10.3390/biology11040540
Received: 6 March 2022 / Revised: 25 March 2022 / Accepted: 25 March 2022 / Published: 31 March 2022
(This article belongs to the Special Issue Theories and Models on COVID-19 Epidemics)
In the past two years, the COVID-19 incidence curves and reproduction number Rt have been the main metrics used by policy makers and journalists to monitor the spread of this global pandemic. However, these metrics are not always reliable in the short term, because of a combination of delay in detection, administrative delays and random noise. In this article, we present a complete model of COVID-19 incidence, faithfully reconstructing the incidence curve and reproduction number from the renewal equation of the disease and precisely estimating the biases associated with periodic weekly bias, festive day bias and residual noise.
The sanitary crisis of the past two years has focused the public’s attention on quantitative indicators of the spread of the COVID-19 pandemic. The daily reproduction number Rt, defined by the average number of new infections caused by a single infected individual at time t, is one of the best metrics for estimating the epidemic trend. In this paper, we provide a complete observation model for sampled epidemiological incidence signals obtained through periodic administrative measurements. The model is governed by the classic renewal equation using an empirical reproduction kernel, and subject to two perturbations: a time-varying gain with a weekly period and a white observation noise. We estimate this noise model and its parameters by extending a variational inversion of the model recovering its main driving variable Rt. Using Rt, a restored incidence curve, corrected of the weekly and festive day bias, can be deduced through the renewal equation. We verify experimentally on many countries that, once the weekly and festive days bias have been corrected, the difference between the incidence curve and its expected value is well approximated by an exponential distributed white noise multiplied by a power of the magnitude of the restored incidence curve. View Full-Text
Keywords: incidence curve; pandemic; COVID-19; reproduction kernel; time dependent reproduction number; administrative noise; exponential distribution; renewal equation; variational inversion method incidence curve; pandemic; COVID-19; reproduction kernel; time dependent reproduction number; administrative noise; exponential distribution; renewal equation; variational inversion method
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MDPI and ACS Style

Alvarez, L.; Morel, J.-D.; Morel, J.-M. Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise. Biology 2022, 11, 540. https://doi.org/10.3390/biology11040540

AMA Style

Alvarez L, Morel J-D, Morel J-M. Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise. Biology. 2022; 11(4):540. https://doi.org/10.3390/biology11040540

Chicago/Turabian Style

Alvarez, Luis, Jean-David Morel, and Jean-Michel Morel. 2022. "Modeling COVID-19 Incidence by the Renewal Equation after Removal of Administrative Bias and Noise" Biology 11, no. 4: 540. https://doi.org/10.3390/biology11040540

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