Modeling of COVID-19 propagation with compartment models.

Q4 Mathematics Mathematische Semesterberichte Pub Date : 2021-01-01 Epub Date: 2021-11-03 DOI:10.1007/s00591-021-00312-9
Günter Bärwolff
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Abstract

The current pandemic is a great challenge for several research areas. In addition to virology research, mathematical models and simulations can be a valuable contribution to the understanding of the dynamics of the pandemic and can give recommendations to both physicians and politicians. In this paper we give an overview about mathematical models to describe the pandemic by differential equations. As a matter of principle the historic origin of the epidemic growth models will be remembered. Moreover we discuss models for the actual pandemic of 2020/2021. This will be done based on actual data of people infected with COVID-19 from the European Centre for Disease Prevention and Control (ECDC), input parameters of mathematical models will be determined and applied. These parameters will be estimated for the UK, Italy, Spain, and Germany and used in a SIR-type model. As a basis for the model's calibration, the initial exponential growth phase of the COVID-19 pandemic in the named countries is used. Strategies for the commencing and ending of social and economic shutdown measures are discussed. To respect heterogeneity of the people density in the different federal states of Germany diffusion effects are considered.

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利用分区模型对 COVID-19 的传播进行建模。
当前的大流行病对多个研究领域都是一个巨大的挑战。除了病毒学研究外,数学模型和模拟也能为了解大流行病的动态做出宝贵贡献,并为医生和政治家提供建议。本文概述了用微分方程描述大流行病的数学模型。原则上,我们将回顾流行病增长模型的历史渊源。此外,我们还将讨论 2020/2021 年实际流行病的模型。我们将根据欧洲疾病预防和控制中心(ECDC)提供的 COVID-19 感染者的实际数据,确定并应用数学模型的输入参数。将为英国、意大利、西班牙和德国估算这些参数,并将其用于 SIR 型模型。作为模型校准的基础,将使用 COVID-19 大流行在上述国家的初始指数增长阶段。讨论了社会和经济关闭措施的开始和结束策略。为尊重德国不同联邦州人口密度的异质性,考虑了扩散效应。
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来源期刊
Mathematische Semesterberichte
Mathematische Semesterberichte Mathematics-Mathematics (all)
CiteScore
0.40
自引率
0.00%
发文量
18
期刊介绍: Die „Mathematischen Semesterberichte“ wurden im Jahre 1932 durch Heinrich Behnke und Otto Toeplitz gegründet. Sie enthalten einerseits Berichte aus der Forschung über interessante neue Entwicklungen in der Mathematik und ihren Anwendungen; andererseits behandeln sie grundlegende fachdidaktische Fragen des Lehrens und Lernens von Mathematik an Schule und Hochschule. Diese beiden Ziele verbinden sich in der Auseinandersetzung mit Problemen und Querverbindungen in der Mathematik sowie in Beiträgen zur historischen Entwicklung und zu den Grundlagen der Mathematik. Auf einen klaren, motivierenden Stil der Beiträge wird besonderer Wert gelegt. Die Zeitschrift umfasst die Rubriken "Mathematische Bildergalerie", "Mathematik in Forschung und Anwendung", "Mathematik in der Lehre", "Dokumente", sowie "Philosophische und Historische Sicht". Die zusätzliche Rubrik "Buchbesprechungen" präsentiert und kritisiert neuerschienene Bücher von allgemeinem Interesse. ______ The "Mathematische Semesterberichte" were founded in 1932 by Heinrich Behnke and Otto Toeplitz. On the one hand, they contain reports from research about interesting new developments in mathematics and its applications; on the other hand, they deal with fundamental questions of teaching and learning mathematics at school and at institutions of higher education. These two goals are combined in the examination of problems and cross-connections in mathematics as well as in contributions on the historical development and foundations of mathematics. Special emphasis is placed on a clear, motivating style of the contributions. The journal includes the sections "Mathematical Imagery," "Mathematical Research and Applications," "Teaching Mathematics," "Documents", and "Philosophical and Historical Perspectives." The additional section "Book Review" presents and critiques recently published books of general interest.
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