key: cord-0849085-sai7ysuo
authors: Hu, F.-C.
title: The Estimated Time-Varying Reproduction Numbers during the Ongoing Pandemic of the Coronavirus Disease 2019 (COVID-19) in 12 Selected Countries outside China
date: 2020-05-14
journal: nan
DOI: 10.1101/2020.05.10.20097154
sha: c75d0f053c254c8fd69636e459adca0ff72a0552
doc_id: 849085
cord_uid: sai7ysuo

Background: How can we anticipate the progression of the ongoing pandemic of the coronavirus disease 2019 (COVID-19)? As a measure of transmissibility, we aimed to estimate concurrently the time-varying reproduction number, R0(t), over time during the COVID-19 pandemic for each of the following 12 heavily-attacked countries: Singapore, South Korea, Japan, Iran, Italy, Spain, Germany, France, Belgium, United Kingdom, the United States of America, and South Africa. Methods: We downloaded the publicly available COVID-19 pandemic data from the WHO COVID-19 Dashboard website (https://covid19.who.int/) for the duration of January 11, 2020 and May 1, 2020. Then, we specified two plausible distributions of serial interval to apply the novel estimation method implemented in the incidence and EpiEstim packages to the data of daily new confirmed cases for robustly estimating R0(t) in the R software. Results: We plotted the epidemic curves of daily new confirmed cases for the 12 selected countries. A clear peak of the epidemic curve appeared in 10 of the 12 selected countries at various time points, and then the epidemic curve declined gradually. However, the United States of America and South Africa happened to have two or more peaks and their epidemic curves either reached a plateau or still climbed up. Almost all curves of the estimated R0(t) monotonically went down to be less than or close to 1.0 up to April 30, 2020 except Singapore, South Korea, Japan, Iran, and South Africa, of which the curves surprisingly went up and down at various time periods during the COVID-19 pandemic. Finally, the United States of America and South Africa were the two countries with the approximate R0(t) [≥] 1.0 at the end of April, and thus they were now facing the harshest battles against the coronavirus among the 12 selected countries. By contrast, Spain, Germany, and France with smaller values of the estimated R0(t) were relatively better than the other 9 countries. Conclusion: Seeing the estimated R0(t) going downhill speedily is more informative than looking for the drops in the daily number of new confirmed cases during an ongoing epidemic of infectious disease. We urge public health authorities and scientists to estimate R0(t) routinely during an epidemic of infectious disease and to report R0(t) daily to the public until the end of the epidemic.

result. 2 Then, we started this investigation on April 4, 2020 with the aim to estimate concurrently the time-varying reproduction number, R0(t), over time during the ongoing COVID-19 pandemic for each of the following 12 heavily-attacked countries in different continents: (1) Singapore, (2) Republic of Korea (i.e., South Korea), (3) Japan, (4) Islamic Republic of Iran (i.e., Iran), (5) Italy, (6) Spain, (7) Germany, (8) France, (9) Belgium, (10) United Kingdom, (11) the United States of America, and (12) South Africa.

To collect all individual patient data, including personal contact history, during an epidemic is a tough and crucial task. As revealed in the report of the Novel Coronavirus Pneumonia Emergency Response Epidemiology Team, great efforts have previously been made in China to build up China's Infectious Disease Information System, which is very helpful in the management of nationwide patient data during this epidemic of a large size. 5 Such highly confidential and miscellaneous data are not global-data.csv") from the WHO COVID-19 Dashboard website (https://covid19.who.int/), 3 for the duration of January 11, 2020 and May 1, 2020 (Last Updated: 2020/5/1, 3:00 PM CEST) in this study.

Statistical analysis was performed using the R 3.6.3 software (R Foundation for Statistical Computing, Vienna, Austria). The distributional properties of daily counts of new confirmed cases were presented by the number of days (n), total number, mean, standard deviation (SD), minimum, the first quartile (Q1), median, the third quartile (Q3), and maximum for each of the 12 selected countries outside China.

Instead of developing any advanced methods specific for this pandemic, we tried to find an available easy-to-use tool to monitor the progress of the ongoing COVID-19 pandemic as soon as possible. As listed on the Comprehensive R Archive Network (CRAN) (https://cran.r-project. org/), several R packages might be used to compute basic reproduction numbers of an epidemic in R, including argo, epibasix, EpiCurve, EpiEstim, EpiILM, EpiILMCT, epimdr, 6 epinet, epiR, EpiReport, epitools, epitrix, incidence, mem, memapp, R0, and surveillance. We chose the incidence (version 1.7.0) and EpiEstim (version 2.2-1) packages to estimate R0(t) in R during the ongoing COVID-19 pandemic for the 12 selected countries outside China due to their methodological soundness and computational simplicity for rapid analysis. 7,8 The R code was listed in the Supplementary Appendix of our previous study of China 2 for check and re-uses.

First, we laid out the conceptual framework below. In an epidemic of infectious disease, any susceptible subject who becomes a patient usually goes through the following three dynamic stages: infection, development of symptoms, and diagnosis of the disease. Theoretically, to estimate R0 or R0(t), we need the information about . 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.

The copyright holder for this preprint this version posted May 14, 2020. . https://doi.org/10.1101/2020.05.10.20097154 doi: medRxiv preprint the distribution of generation time (GT), which is the time interval between the infection of the index case and the infection of the next case infected directly from the index case. 8 Yet, the time of infection is most likely unavailable or inaccurate, and thus investigators collect the data about the distribution of serial interval (SI) instead, which is the time interval between the symptom onset of the index case and the symptom onset of the next case infected directly from the index case. 8 Nevertheless, the data of symptom onset are not publically available and almost always have the problem of delayed reporting in any ongoing epidemic of infectious disease because they are usually recorded at diagnosis. 5 Hence, we took a common approach in statistics to tackle this problem by specifying the best plausible distributions of SI according to the results obtained from previous studies of similar epidemics, and then applied the novel estimation method implemented in the EpiEstim package to the data of daily new confirmed cases in practice. 7, 8 Next, we considered two plausible scenarios for studying the ongoing COVID-19 pandemic in the 12 selected countries outside China. The estimate_R function of the EpiEstim package assumes a Gamma distribution for SI by default to approximate the infectivity profile. 7 Technically, the transmission of an infectious disease is modeled with a Poisson process in the EpiEstim package. 7,8 When we choose a Gamma prior distribution for SI, the Bayesian statistical inference leads to a simple analytical expression for the Gamma posterior distribution of R0(t). 8 In the first scenario, we specified the mean (SD) of the Gamma distribution for SI to be 8.4 (3.8) days to mimic the 2003 epidemic of the severe acute respiratory syndrome (SARS) in Hong Kong. 8 Then, in the second scenario, we specified the mean (SD) of the Gamma distribution for SI to be 2.6 (1.5) days to mimic the 1918 pandemic of influenza in Baltimore, Maryland. 8 According to the current understanding, the transmissibility of . 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 May 14, 2020. . https://doi.org/10.1101/2020.05.10.20097154 doi: medRxiv preprint COVID-19 was higher than SARS but lower than influenza. 1 Hence, even though we did not know the true distribution(s) of SI for the ongoing pandemic of COVID-19 in the 12 selected countries outside China, these two plausible scenarios helped us catch the behavior pattern of this pandemic along with the time evolution.

We subtracted one day from the reporting dates in the COVID-19 pandemic data of WHO to obtain the "dates" on which the daily new confirmed cases actually occurred. Then, we computed the sample statistics of the daily new confirmed cases for the 12 selected countries over the time period from January 10, 2020 to April 30, 2020 in Table 1 . The starting date of the COVID-19 epidemic differed among the 12 countries so that the sample size (i.e., number of days) varied from 58 (South Africa) to 109 (Japan). All the daily new confirmed cases in the 12 selected countries were laboratory confirmed, but the number of daily new confirmed cases included both domestic and repatriated cases according to the description of WHO. 4 As expected, the larger the mean value of daily new confirmed cases, the bigger the size of the corresponding SD. Spain, France, Belgium, and the United States of America had zero-valued Q1's, indicating that they had zero daily new confirmed case in the early phase of the pandemic for more than 25 days but the number of daily new confirmed cases were soaring quickly after then. These sample statistics revealed the magnitudes of the ongoing COVID-19 pandemic in each of the 12 selected countries over the study period. Surprisingly, the United States of America had a total of 1,035,353 new confirmed cases accumulated over 103 days up to April 30, 2020 and it became the severest epidemic area in the world.

. 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 May 14, 2020. 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 May 14, 2020. . https://doi.org/10.1101/2020.05.10.20097154 doi: medRxiv preprint mobility, to contain the second and third waves of the COVID-19 epidemic. In particular, the effectiveness of these stringent control measures had led to a sharp drop in the estimated R0(t) to bring it down to below 1.0 in the last two weeks of April.

This was a rarely seen victory in the places outside China, and thus it would be very encouraging to the countries with gently sloped curves for the last several weeks before April 30, 2020 such as South Korea, Japan, Iran, Italy, Spain, Germany, France, Belgium, United Kingdom, and the United States of America. 

. 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.

The copyright holder for this preprint this version posted May 14, 2020. . https://doi.org/10.1101/2020.05.10.20097154 doi: medRxiv preprint Almost everyone is susceptible to the novel COVID-19 and this is one of the reasons why the COVID-19 epidemic occurs in many places and has caused public panics worldwide. In terms of population size, the depletion due to death or recovery might be negligible in big countries such as China, but not in small ones such as 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.

The copyright holder for this preprint this version posted May 14, 2020. is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 14, 2020. . https://doi.org/10.1101/2020.05.10.20097154 doi: medRxiv preprint Singapore, the SI tended to be shorter after control measures were implemented. 18 The SI also depended on the amount of infecting dose, the level of host immunity, and the intensity of person-to-person contacts. 16 To summarize, most of these limitations led our estimation of R0(t) into a more conservative context.

Looking at the epidemic curves of the 12 selected countries in Figures 1-1 Although it is difficult to estimate the exact date when it will happen, the peak can only appear after the trend of the computed R0(t) is declining sharply and monotonically for some days (e.g., about 10 days in China), and then the daily number of new confirmed cases will begin dropping, indicating that the COVID-19 epidemic has abated. However, it is very frustrating to see the curve of the estimated is the author/funder, who has granted medRxiv a license to display the preprint in perpetuity.

The copyright holder for this preprint this version posted May 14, 2020. . https://doi.org/10.1101/2020.05.10.20097154 doi: medRxiv preprint infectious disease dynamics to epidemic data with limited information about required parameters is a challenge. 6, 8, [24] [25] [26] The results of such analyses may be difficult to generalize due to the context-specific assumptions made and it can be too slow to meet a pressing need during an epidemic. 8,18,27-34 Thus, an easy-to-use pragmatic tool such as the estimated R0(t) for monitoring the COVID-19 pandemic is so important in practice. Although this study could not provide the most accurate results rigorously, it sufficed for the pragmatic purpose from the public health viewpoint. We believed that it was an approximate answer to the right question timely. Refinements in the estimation of R0(t) can be made with the individual patient data, including personal contact history, whenever they are available for analysis.

Since the coronavirus has spread out globally, we should take the important lessons from China, 2,20-23,31-34 South Korea, 35 Italy, 36 the United States of America, 37, 38 and Singapore 39 and learn the experiences from the previous epidemics 1,25 to mitigate its harm as much as possible. We may also use China as an example to anticipate the potential progression of the COVID-19 pandemic in a particular country. 2 As listed in Appendix, control tactics and measures should be applied in line with local circumstances, 25 but the same easy-to-use monitoring tool, R0(t), can be applied to many places. Such timely available information for monitoring the ongoing VOVID-19 pandemic deserves societal attention, especially when the government is going to make a move in the harsh battle against the coronavirus. As the coronavirus outbreak continues to spread, let's help each other to combat the COVID-19 pandemic together.

After all, we are all in the same shaking boat now.

The authors did not receive any funding for this study. The corresponding author . 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.

The copyright holder for this preprint this version posted May 14, 2020. . https://doi.org/10.1101/2020.05.10.20097154 doi: medRxiv preprint had full access to all the data in the study and had final responsibility for the decision to submit for publication.

We declared no conflicts of interest in this study. . 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.

The copyright holder for this preprint this version posted May 14, 2020. (URL: https://edition.cnn.com/2020/04/18/asia/singapore-coronavirus-responseintl-hnk/index.html)

. 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.

The copyright holder for this preprint this version posted May 14, 2020. Abbreviation: Q1 = the first quartile, Q3 = the third quartile, and SD = standard deviation. Abbreviation: SD = standard deviation. Appendix: The source-transmission-host approach to controlling the COVID-19 pandemic.

1. Goal: The "Separation" Process.

As depicted in the following diagram, what we should do to control the COVID-19 epidemic within a black rectangle (e.g., a city, a state, or a country) is to separate the red balls (i.e., patients) from the grey circles (i.e., medical personnel) and the green balls (healthy subjects). When the number of new cases is soaring in Stage 2, the more aggressive separation process is needed by reducing population mobility, implementing mass testings, and conducting community surveillance. We ask or force the red balls to enter the big grey circle(s) as in Stage 3. Reporting and announcements (e.g., risk sources, locations, and pathways)

Lockdowns (short-term or long-term) Vaccination 5 (Not available yet, but scientists are developing COVID-19 vaccines now)

Information release and sharing (e.g., risk sources, locations, and pathways)

Long-term follow-ups of recovered cases

Preparation for possible sustained transmission of 2019 novel coronavirus: Lessons from previous epidemics

The estimated time-varying reproduction numbers during the ongoing epidemic of the coronavirus disease 2019 (COVID-19) in China. medRxiv

COVID-19). Dashboard. Geneva: World Health Organization

Situation reports. Geneva: World Health Organization

A novel coronavirus emerging in China -Key questions for impact assessment

Presumed asymptomatic carrier transmission of COVID-19

Serial interval of novel coronavirus (COVID-19) infections

Temporal dynamics in viral shedding and transmissibility of COVID-19

Different epidemic curves for severe acute respiratory Figure 10-1. The epidemic curve of the coronavirus disease 2019 (COVID-19) in the United Kingdom from