Article
Version 2
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Defining and Computing Reproduction Numbers to Monitor the Outbreak of Covid-19 or Other Epidemics
Version 1
: Received: 29 June 2020 / Approved: 30 June 2020 / Online: 30 June 2020 (11:40:43 CEST)
Version 2 : Received: 15 February 2021 / Approved: 16 February 2021 / Online: 16 February 2021 (13:18:54 CET)
Version 2 : Received: 15 February 2021 / Approved: 16 February 2021 / Online: 16 February 2021 (13:18:54 CET)
How to cite: Zingano, P.; Zingano, J.; Silva, A.; Zingano, C. Defining and Computing Reproduction Numbers to Monitor the Outbreak of Covid-19 or Other Epidemics. Preprints 2020, 2020060370 (doi: 10.20944/preprints202006.0370.v2). Zingano, P.; Zingano, J.; Silva, A.; Zingano, C. Defining and Computing Reproduction Numbers to Monitor the Outbreak of Covid-19 or Other Epidemics. Preprints 2020, 2020060370 (doi: 10.20944/preprints202006.0370.v2).
Abstract
We present a general approach to define reproduction ratios or numbers to monitor the outbreak of epidemics that are modeled by mathematical evolution equations. This provides a solution to an important topic that has not been completely settled in the literature, especially in the case of complex epidemiological models. We illustrate our procedure with a full implementation of a standard deterministic SEIR model that is applied to examine the Covid-19 outbreaks and the effects of intervention measures in several countries in America (Argentina, Brazil, Mexico, USA) and Europe (France, Italy, Spain and UK) in 2020. Our code is also used to investigate herd immunity levels for Covid-19, indicating values between 85% and 90%.
Supplementary and Associated Material
https://drive.google.com/drive/folders/16kLxlZyqH-QATOLQI6QWTx7qZnL3IoCP: repository of computer program for free download
https://www.worldometers.info/coronavirus/: source of data for the computations
https://covid.saude.gov.br/: alternative source of data for the computations regarding Brazil
Keywords
Covid-19 outbreak; SARS-Cov-2 coronavirus; reproduction numbers; SEIR models; parameter determination; herd immunity against Covid-19
Subject
MATHEMATICS & COMPUTER SCIENCE, Computational Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (1)
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Commenter: Paulo Zingano
Commenter's Conflict of Interests: Author
(1) a discussion of the INITIALIZATION PROBLEM for the SEIR model (Section 2), not covered before;
(2) an updated description of the evolution of the Covid-19 epidemic in the 8 countries chosen, now covering the entire year (2020) and including the original predictions made on June/2020 for comparison purposes;
(3) estimation of herd immunity levels for covid-19 in 2 distinct scenarios (unwarned/warned populations);
(4) an updated bibliography (following referee's suggestions)