Universality in COVID-19 spread in view of the Gompertz function
Akira Ohnishi, Yusuke Namekawa, Tokuro Fukui
Abstract
Abstract We demonstrate that universal scaling behavior is observed in the current coronavirus (SARS-CoV-2) spread, the COVID-19 pandemic, in various countries. We analyze the numbers of infected people who tested positive (cases) in 11 selected countries (Japan, USA, Russia, Brazil, China, Italy, Indonesia, Spain, South Korea, UK, and Sweden). By using a double exponential function called the Gompertz function, $f_\mathrm{G}(x)=\exp(-e^{-x})$, the number of cases is well described as $N(t)=N_0 f_\mathrm{G}(\gamma(t-t_0))$, where $N_0$, $\gamma$, and $t_0$ are the final number of cases, the damping rate of the infection probability, and the peak time of the daily number of new cases, $dN(t)/dt$, respectively. The scaled data of cases in most of the analyzed countries are found to collapse onto a common scaling function $f_\mathrm{G}(x)$ with $x=\gamma(t-t_0)$ being the scaling variable in the range of $f_\mathrm{G}(x)\pm 0.05$. The recently proposed indicator, the so-called $K$ value, the increasing rate of cases in one week, is also found to show universal behavior. The mechanism for the Gompertz function to appear is discussed from the time dependence of the produced pion numbers in nucleus–nucleus collisions, which is also found to be described by the Gompertz function.