Doubling Time of the COVID-19 Epidemic by Chinese Province

COVID-19 epidemic doubling time by Chinese province was increasing from January 20 through February 9, 2020. The harmonic mean of the arithmetic mean doubling time estimates ranged from 1.4 (Hunan, 95% CI, 1.2–2.0) to 3.1 (Xinjiang, 95% CI, 2.1–4.8), with an estimate of 2.5 days (95% CI, 2.4–2.6) for Hubei.


Additional information on our motivation, scope and methods
Motivation. R0 is a widely used indicator of transmission potential in a totally susceptible population and is driven by the average contact rate and the mean infectious period of the disease (1). Yet, it only characterizes transmission potential at the onset of the epidemic and varies geographically for a given infectious disease according to local healthcare provision, outbreak response, as well as socioeconomic and cultural factors. Furthermore, estimating R0 requires information about the natural history of the infectious disease. Thus, our ability to estimate reproduction numbers for novel infectious diseases is hindered by the paucity of information about their epidemiological characteristics and transmission mechanisms. More informative metrics could synthesize real-time information about the extent to which the epidemic is expanding over time. Such metrics would be particularly useful if they rely on minimal data on the outbreak's trajectory (2).
Scope and definition. Our analysis is restricted to mainland China in this paper. A 'province' herein encompasses three different types of political sub-divisions of mainland China, namely, a province, a centrally (literally, 'directly') administered municipality (Beijing, Chongqing, Shanghai, and Tianjin) and an 'ethnic minority' autonomous region (Guangxi, Inner Mongolia, Ningxia, Tibet, and Xinjiang). Our analysis does not include the Hong Kong Special Administrative Region and the Macau Special Administrative Region, which are under the effective rule of the People's Republic of China through the so-called 'One Country, Two Systems' political arrangements. Likewise, our analysis does not include Taiwan, which is de facto governed by a different government (the Republic of China).
Data sources. Daily cumulative incidence data were retrieved from provincial health commissions' websites (Table S8). Data were double-checked against the cumulative national total published by the National Health Commission (3), data compiled by the Centre for Health Protection, Hong Kong, when . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted April 24, 2020. . https://doi.org/10.1101/2020.02.05.20020750 doi: medRxiv preprint available (4) and by John Hopkins University Center for Systems Science and Engineering (5). Whenever discrepancies arose, provincial government sources were deemed authoritative.

Doubling time calculation and its relationship with growth rate of an epidemic
As the epidemic grows, the times at which cumulative incidence doubles are given by such that where , , and i = 0,1,2,3, …, nd where is the total number of times cumulative incidence doubles. The actual sequence of "doubling times" are defined as follows: where j = 1,2,3, …, nd.
To quantify parameter uncertainty, we used parametric bootstrapping with a Poisson error structure around the harmonic mean of doubling times to obtain the 95% confidence interval. See references (6)(7)(8) for further details.
Additional details on methods. Doubling time calculation was conducted using MATLAB R2019b (Mathworks, Natick, MA). Figures were created either using R version 3.6.2 (R Core Team) or MATLAB 2019b. Significance level in this manuscript was a priori decided to be α = 0.05.

Additional information on our results and discussion
Cumulative incidence over time. From Figure S7 to Figure S10, we provided plots of cumulative incidence over time (left panel) and semi-log plots with log10-transformed cumulative incidence over time . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

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The copyright holder for this preprint this version posted April 24, 2020. . https://doi.org/10.1101/2020.02.05.20020750 doi: medRxiv preprint (right panel) for a total of 8 provinces with a relatively high number of cases, namely, the epicenter Hubei, followed by (in alphabetical order) Fujian, Guangdong, Heilongjiang, Henan, Hubei, Hunan, Jiangxi and Shandong. If the epidemic is growing exponentially, the log10-transformed cumulative incidence over time will be a linear curve. If social distancing would have an impact, the slope of the semi-log plot would decrease, indicating a decreasing epidemic growth rate.
Harmonic mean of the harmonic mean. In this study, we also presented the harmonic mean of the harmonic means of the estimates of the epidemic doubling times. The harmonic means of the epidemic doubling times are shorter than their arithmetic means. From January 20 through February 9, the harmonic mean of the harmonic means of the doubling times estimated ranged from 0. 5  Further discussion. The slowing-down of the epidemic as represented in increasing epidemic doubling times in our study is also consistent with a study by Benjamin F. Maier and Dirk Brockmann, "Effective containment explains sub-exponential growth in confirmed cases of recent COVID-19 outbreak in Mainland China" (pre-print available at arXiv. 2020:2002.07572). They also identified sub-exponential growth of the outbreak across provinces, as mass quarantine and restriction of travels across mainland China began since January 23, 2020.
Sensitivity analysis #1. We performed a sensitivity analysis by expanding our data analysis to the data since December 31, 2019, when Hubei first reported a cluster of pneumonia cases with unexplained etiology that turned out to be COVID-19. The only difference between the sensitivity analysis and the main analysis is the inclusion of Hubei and Guangdong data from December 31, 2019, through January 19, 2020, because nationwide reporting started on January 20, 2020. The only differences in results were found for Hubei and Guangdong. For Hubei, the harmonic mean of the arithmetic mean of the doubling . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity. (which was not certified by peer review) The copyright holder for this preprint this version posted April 24, 2020. . https://doi.org/10.1101/2020.02.05.20020750 doi: medRxiv preprint times was 4.06 (95% CI, 3.85-4.33); the harmonic mean of the harmonic means of the doubling times for Hubei was 2.28 (95% CI, 2.08-2.56); and the cumulative incidence in Hubei doubled nine times from December 31, 2019, through February 9, 2020 (Table S5, Figures S3, S4, S12, S13, S14). The first doubling time of Hubei ( Figure S3) was high, reflecting that real-time data was unavailable before mid-January. It was only by January 17, 2020, onwards when data reporting become increasingly transparent and timely.
Sensitivity analysis #2. We also performed a sensitivity analysis by restricting our data analysis to the data from January 23, 2020 through February 9, 2020, to allow for the time that all the other provinces to ramp up their testing. January 23 was also the day when the Chinese authorities to put the city of Wuhan on 'lockdown' and major inter-provincial travel restrictions were put in place. When we changed the start date of our study period from January 20 (main analysis) to January 23, 2020 (sensitivity analysis #2), the epidemic doubling time of the aggregate cumulative incidence of mainland China (except Hubei)  Figure S5, S6). Apart from the epidemic doubling time of the aggregate cumulative incidence of mainland China (except Hubei), we did not observe significant differences by province between results in the main analysis and sensitivity analysis #2. Therefore, our results should be robust for the purpose of this study.

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The copyright holder for this preprint this version posted April 24, 2020. . https://doi.org/10.1101/2020.02.05.20020750 doi: medRxiv preprint Figure S1. Main analysis: The harmonic mean of the arithmetic means of COVID-19 epidemic doubling times (red circle) with 95% confidence interval (red bar) of the doubling times (days), and their values (black diamond) by the number of times the reported cumulative incidence doubles by province within mainland China from January 20, 2020 through February 9, 2020. Each panel represents a province except the panel representing "Mainland China (except Hubei)" that is the aggregate of all other provinces in mainland China, except Hubei. Doubling time for Tibet is not available, because there had only been 1 confirmed case in Tibet as of February 9, 2020.     . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted April 24, 2020.       . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted April 24, 2020.   CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted April 24, 2020. . https://doi.org/10.1101/2020.02.05.20020750 doi: medRxiv preprint . CC-BY-NC-ND 4.0 International license It is made available under a is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

(which was not certified by peer review)
The copyright holder for this preprint this version posted April 24, 2020.