Power Law in COVID-19 Cases in China

Abstract

The novel coronavirus (COVID‐19) was first identified in China in December 2019. Within a short period of time, the infectious disease has spread far and wide. This study focuses on the distribution of COVID‐19 confirmed cases in China—the original epicentre of the outbreak. We show that the upper tail of COVID‐19 cases in Chinese cities is well described by a power law distribution, with exponent around one in the early phases of the outbreak (when the number of cases was growing rapidly) and less than one thereafter. This finding is significant because it implies that (i) COVID‐19 cases in China is heavy tailed and disperse; (ii) a few cities account for a disproportionate share of COVID‐19 cases; and (iii) the distribution generally has no finite mean or variance. We find that a proportionate random growth model predicated by Gibrat's law offers a plausible explanation for the emergence of a power law in the distribution of COVID‐19 cases in Chinese cities in the early phases of the outbreak.

The impact of a power law-induced memory effect on the SARS-CoV-2 transmission

“…As power law/memory effect in disease transmission is directly related to some forced COVID-19 control measures like lockdown, social distancing, use of face-mask, therefore, using these measures may control future waves in these locations. These findings agree with some recent results of the power law effect on COVID-19 incidence growth pattern [8] , [13] , [77] , [78] , [79] . Therefore, government and policymakers may focus on restricting and to restrict the forthcoming waves in these four locations (see Figs.…”

“…By analyzing COVID-19 incidence data from different countries around the globe, several studies concluded that at the beginning of the epidemic, data trends followed some exponential growth, and as the epidemic progress over the years, data trended to exhibit a power law growth pattern [8] , [9] , [10] , [11] , [13] , [77] , [78] , [79] . In general, power law growth in COVID-19 cases is directly related to control measures, in the sense that the less strict the control, the smaller the power law exponent, and hence the slower the disease progresses to its end [8] , [13] , [77] , [77] , [78] , [79] . Thus, it is reasonable to assume that the COVID-19 transmission process follows some power law [79] .…”

“…In general, power law growth in COVID-19 cases is directly related to control measures, in the sense that the less strict the control, the smaller the power law exponent, and hence the slower the disease progresses to its end [8] , [13] , [77] , [77] , [78] , [79] . Thus, it is reasonable to assume that the COVID-19 transmission process follows some power law [79] . Recently, several studies established that fractional derivatives (Riemann–Liouville and Caputo) and integrals are convoluted with a power law [17] , [18] , [19] , [80] , [81] , where the order of the fractional derivative ( ) represents the power law exponent [21] .…”

The distribution of COVID-19 mortality

“…There have been some papers studying the distribution of caseloads for COVID-19 during the early phases of the pandemic ( Beare & Toda, 2020 ; Blasius, 2020 ; Chan et al, 2021 ; Komarova et al, 2020 ; Singer, 2020 ; Vazquez, 2020 ). Beare and Toda (2020) ; Blasius (2020) ; Komarova et al (2020) ; Singer (2020) ; Vazquez (2020) ; Ahundjanov et al (2022) have found some evidence of a power-law distribution in the number of COVID-19 cases. Chan et al (2021) found a negative binomial was the best fitting count regression model to COVID-19 case counts.…”

Time series analysis and short-term forecasting of monkeypox outbreak trends in the 10 major affected countries

“…Additionally [ 34 ], proposed a new zero-state coupled Markov switching negative binomial model in which the disease alternates between periods of presence and absence in each area using a series of partially hidden nonhomogeneous Markov chains coupled between nearby locations. The distribution of COVID-19 confirmed cases in China was examined by [ 35 ] With respect to the dynamics of Power law.…”