Universality in COVID-19 spread in view of the Gompertz function

Abstract

We demonstrate that universal scaling behavior is observed in the current coronavirus (COVID-19) spread in various countries. We analyze the numbers of infected people in selected eleven countries (Japan, USA, Russia, Brazil, China, Italy, Indonesia, Spain,South Korea, UK, and Sweden). By using the double exponential function called the Gompertz function, fG(x)=exp(−e−x), the number of infected people is well described as N(t)=N0 fG(γ(t−t0)), where N0, γ and t0 are the final total number of infected people, the damping rate of the infection probability and the peak time of dN(t)/dt, respectively. The scaled data of infected people in most of the analyzed countries are found to collapse onto a common scaling function fG(x) with x=γ(t−t0) in the range of fG(x) ± 0.05. The recently proposed indicator so-called the K value, the increasing rate of infected people 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.

Characterizing and Managing an Epidemic: A First Principles Model and a Closed Form Solution to the Kermack and McKendrick Equations

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A Statistical Analysis of Death Rates in Italy for the Years 2015–2020 and a Comparison with the Casualties Reported from the COVID-19 Pandemic

“…While the excess peaks look highly symmetrical around their maximum and can thus be reasonably well modeled with Gaussians, as described before, the peak of the spring 2020, associated with the COVID-19 pandemic, is clearly asymmetric. We have tried several possible parametrizations for that distribution, such as bifurcated Gaussians with a common peak, generalized logistics, or else, to reflect the asymmetry, but in the end we resolved to adopt the derivative of a Gompertz function [ 19 , 20 ] simply because it is customarily adopted by epidemiologists to describe epidemic evolution’s over time and we therefore considered it more suitable to our purpose.…”

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“…Covid-19 mortality above age 20 follows everywhere the so-called Gompertz law of mortality (in which death rates can be expressed as an exponential function of age). 23 24 25 As a result of this strong mathematical regularity, death rates unknown at one given age can be extrapolated from death rates observed at other ages. Another advantage of the Gompertz modeling is its partition of mortality into two main components: its age gradient (i.e., the slope, or the tempo of mortality) that corresponds to variations by age, and its intensity (the level or quantum of mortality) that captures the overall severity at all ages.…”