论文标题
SIR型数学模型的前景和限制捕获COVID-19大流行
Prospects and limits of SIR-type Mathematical Models to Capture the COVID-19 Pandemic
论文作者
论文摘要
对于大流行数学模型的描述可能很有趣。对于医生和政客来说，都是治疗这种疾病的决定的基础。负责任的参数估计是数学大流行模型的主要问题。尤其是$β$的好选择，因为一个感染者每天（每天）遇到的其他人的数量会影响模型结果的适当性。对于实际的共同19岁大流行，将讨论参数选择的某些方面。由于约翰·霍普金斯 - 大学数据与德国罗伯特·科赫·伊斯提特（Robert-Koch-Institut）的数据的数据不兼容，因此我们使用欧洲疾病预防与控制中心（ECDC）的COVID-19数据作为参数估计的基础。在本文中将讨论两种不同的数据分析数学方法，并将显示可能的麻烦来源。作为参数选择的例子，可以为美国和英国的数据提供数据。所得参数将用于估计并在w。\ o中使用。 kermack和a。\，g。麦肯德里克的先生模特。讨论了开始和结束社会和经济关闭措施的策略。修改后的SIR模型的普通微分方程系统的数值解决方案是通过第四阶的Runge-Kutta集成方法完成的。最后，可以从本质上显示SIR模型的适用性。关于基于感染加速度的锁定措施开始锁定措施的适当时间点的建议，该论文总结了本文。
For the description of a pandemic mathematical models could be interesting. Both for physicians and politicians as a base for decisions to treat the disease. The responsible estimation of parameters is a main issue of mathematical pandemic models. Especially a good choice of $β$ as the number of others that one infected person encounters per unit time (per day) influences the adequateness of the results of the model. For the actual COVID-19 pandemic some aspects of the parameter choice will be discussed. Because of the incompatibility of the data of the Johns-Hopkins-University to the data of the German Robert-Koch-Institut we use the COVID-19 data of the European Centre for Disease Prevention and Control (ECDC) as a base for the parameter estimation. Two different mathematical methods for the data analysis will be discussed in this paper and possible sources of trouble will be shown. As example of the parameter choice serve the data of the USA and the UK. The resulting parameters will be used estimated and used in W.\,O. Kermack and A.\,G. McKendrick's SIR model. Strategies for the commencing and ending of social and economic shutdown measures are discussed. The numerical solution of the ordinary differential equation system of the modified SIR model is being done with a Runge-Kutta integration method of fourth order. At the end the applicability of the SIR model could be shown essentially. Suggestions about appropriate points in time at which to commence with lockdown measures based on the acceleration rate of infections conclude the paper.
