Macromolecular Theory and Simulations ( IF 1.4 ) Pub Date : 2021-05-24 , DOI: 10.1002/mats.202100020 Hidetaka Tobita 1
1 COVID-19 and Distribution
The year 2020 will be memorized as the year of pandemic. On April 11, 2020, under the state of emergency in Japan, I was staring abstractedly at the website of the Center for Systems Science and Engineering at Johns Hopkins University,[1] listing a large number of the COVID-19 cases by country. Simply because there were so many numbers, I tried the ranking plot, graphically showing the relationship between rank and size. When plotted on a double logarithmic paper, the top countries appear to follow the power law. Since then, my student and I collected the data every week, and Figure 1 shows some examples of the ranking plot.
Equation (3) shows that when the exponent (−α+1) is greater than or equal to −1, the integration goes to infinity, which corresponds to the onset of gelation. The critical value of α is 2. The obtained values shown in Figure 1 are all smaller than 2, which might be interpreted as pandemic.
We found that a simple discrete-time stochastic model[2] that employs the weekly reproduction rate can reproduce the important characteristics of the obtained distribution.[3] On the basis of the model, the necessary conditions to stop the pandemic can also be deduced.
On the other hand, however, the opposite is not always true. Even when a certain mechanistic model can describe the phenomena successfully, this fact does not totally rule out the possibility of other mechanisms. The modeling study is a kind of guessing game, always trying to find out the true culprit. The distribution is a shadow of the stochastic processes.
中文翻译:
发行版
1 COVID-19和发行
2020年将被视为大流行之年。2020年4月11日,在日本处于紧急状态下,我抽象地凝视着约翰·霍普金斯大学系统科学与工程中心的网站,[ 1 ]按国家列出了大量COVID-19案例。仅仅因为有这么多的数字,我尝试了排名图,以图形方式显示了排名和规模之间的关系。当在双对数纸上作图时,排名靠前的国家似乎遵循幂律。从那时起,我和我的学生每周都会收集数据,图 1显示了排名图的一些示例。
等式(3)表明,当指数(-α+ 1)大于或等于-1时,积分达到无穷大,这对应于胶凝的开始。α的临界值为2。图1中显示的所得值均小于2,这可能被解释为大流行。
我们发现,采用每周复制率的简单离散时间随机模型[ 2 ]可以复制获得的分布的重要特征。[ 3 ]在该模型的基础上,还可以推断出停止大流行的必要条件。
但是,另一方面,并非总是如此。即使某个机制模型可以成功地描述现象,该事实也不能完全排除其他机制的可能性。建模研究是一种猜测游戏,总是试图找出真正的罪魁祸首。分布是随机过程的阴影。