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Title: Modeling COVID-19 incidence by the renewal equation after removal of administrative bias and noise
Authors: Alvarez, Luis 
Morel, Jean David
Morel, Jean Michel
UNESCO Clasification: 120601 Construcción de algoritmos
3202 Epidemologia
Keywords: Incidence curve
Reproduction kernel
Time dependent reproduction number, et al
Issue Date: 2022
Journal: Biology 
Abstract: 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.
ISSN: 2079-7737
DOI: 10.3390/biology11040540
Source: Biology [ISSN 2079-7737], n. 11 (4), 540
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