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回归本源：适应新冠疫情的离散 Kermack-McKendrick 模型。

Back to the Roots: A Discrete Kermack-McKendrick Model Adapted to Covid-19.

机构信息

Mathematische Institute der Universitäten Bonn und Frankfurt, Universität Bonn, Bonn, Deutschland.

Faculty of Math./Natural Sciences, and Interdisciplinary Centre for History and Philosophy of Science, University of Wuppertal, Wuppertal, Germany.

出版信息

Bull Math Biol. 2022 Feb 17;84(4):44. doi: 10.1007/s11538-022-00994-9.

DOI:10.1007/s11538-022-00994-9
PMID:35175463
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8853305/
Abstract

A widely used tool for analysing the Covid-19 pandemic is the standard SIR model. It seems often to be used as a black box, not taking into account that this model was derived as a special case of the seminal Kermack-McKendrick theory from 1927. This is our starting point. We explain the setup of the Kermack-McKendrick theory (passing to a discrete approach) and use medical information for specializing to a model called by us an adapted K-McK-model. It includes effects of vaccination, mass testing and mutants. We demonstrate the use of the model by applying it to the development in Germany and show, among others things, that a comparatively mild intervention reducing the time until quarantine by one day would lead to a drastic improvement.

摘要

一种广泛用于分析新冠疫情的工具是标准的 SIR 模型。它似乎经常被当作一个黑盒子，没有考虑到这个模型是从 1927 年开创性的 Kermack-McKendrick 理论中推导出来的一个特例。这就是我们的出发点。我们解释了 Kermack-McKendrick 理论的设置（通过离散方法），并使用医学信息来专门研究我们称之为适应性 K-McK 模型的模型。它包括疫苗接种、大规模检测和突变体的影响。我们通过将其应用于德国的发展来演示模型的使用，并展示了，例如，将隔离时间减少一天的相对温和的干预措施将导致显著的改善。

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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/35c0/8854301/927a86c295ca/11538_2022_994_Fig14_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/35c0/8854301/4de1320f460e/11538_2022_994_Fig1_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/35c0/8854301/69ec2e55e4f6/11538_2022_994_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/35c0/8854301/bcdcb3eb04be/11538_2022_994_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/35c0/8854301/52608068bd62/11538_2022_994_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/35c0/8854301/af0364a08284/11538_2022_994_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/35c0/8854301/a5c8e86e7828/11538_2022_994_Fig10_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/35c0/8854301/54c119fe2494/11538_2022_994_Fig11_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/35c0/8854301/4bba5aa861c9/11538_2022_994_Fig13_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/35c0/8854301/927a86c295ca/11538_2022_994_Fig14_HTML.jpg

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