Doubling time tells how effective Covid-19 prevention works

Doubling time tells how effective Covid-19 prevention works Byung Mook Weon1, 2, ∗ 1Soft Matter Physics Laboratory, School of Advanced Materials Science and Engineering, Sungkyunkwan University, Suwon 16419, South Korea 2Department of Biomedical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA (Dated: March 26, 2020) Abstract Covid-19 (coronavirus disease 2019) is a rapidly spreading pandemic in many countries. The total confirmed cases of Covid-19 are exponentially increasing and many countries are fighting Covid-19 with all strategies. However, there is still lacking consensus for effective strategies. Here, I demonstrate the time dependence of the doubling time in the Covid-19 exponential growths. Tracking the time-dependent doubling time tells how well Covid-19 prevention works, giving an index for successful fighting. ∗Electronic address: [email protected] 1 . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 30, 2020. ; https://doi.org/10.1101/2020.03.26.20044644doi: medRxiv preprint NOTE: This preprint reports new research that has not been certified by peer review and should not be used to guide clinical practice. The Cobid-19 has been spreading rapidly in many countries since it was first discovered in December 2019 [1, 2]. The total confirmed cases of Covid-19 for 12 countries are shown in Fig. 1A, retrieved from the Johns Hopkins University [3]. Each country has more than 4,500 cases as of March 23. The initial growths of the total cases for 12 countries exhibit the exponential growth dynamics, as in Fig. 1B. In general, the exponential growth of the total cases is represented by N = N0 exp(γt) where N0 and N are the total cases at time t0 and t, respectively, and γ is the growth rate. By definition, N = 2N0 needs the doubling time (α) that is expressed as α = ln(2)/γ through ln(N/N0) = ln(2) = γt. If the growth rate evolves with time, depending on the effective prevention strategies, then the doubling time changes with time. Thus, the time-dependent growth rate γ(t) causes the time-dependent doubling time α(t), defined as α(t) = t ln(2)/ ln(N/N0) through γ(t) = ln(N/N0)/t. The doubling time for 12 countries (Fig. 1C) was analyzed (Appendix 1). For China, the doubling time has declined until January 28 and then increased linearly since early Febru- ary, due to the Wuhan containment since January 23. In South Korea, the doubling time has increased linearly without any initial decline. Since the early periods, South Korea has applied effective strategies, such as mass testing and patient tracking, to both symptomatic and asymptomatic patients [4]. The steady increases in the doubling times eventually lead to the flattened total case curves for China and South Korea [2]. In other countries, the increase of the doubling time was not sufficient to flatten the total case curves. The daily increase of the doubling time for 12 countries over the last 10 days (March 14 ∼ March 23) (Fig. 1D) was estimated by linear regression (Appendix 2). In the last 10 days, South Korea and China have the highest daily increases of the doubling time (∼0.14 days per day), eventually achieving the doubling time > 4.0 days. India has ∼0.10 days per day and Austria, Italy, Spain, Netherlands, France, and Switzerland have ∼0.052 days per day (on average), not sufficient to get the flattening (the doubling time < 3.0 days). Finally, Germany, UK, and USA have < 0.03 days per day, implying little change in the doubling time. Little daily increase indicates that the initial exponential growth continues, implying no effective prevention strategies yet. How effective preventive measures work [5] can be evaluated by tracking the doubling time. As demonstrated here, the time-dependent doubling time is real and informative. Successful fighting against Covid-19 would be achievable if the doubling time increases at the rate of ∼0.14 days per day, as seen in South Korea and China. 2 . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 30, 2020. ; https://doi.org/10.1101/2020.03.26.20044644doi: medRxiv preprint Acknowledgments. I would like to thank Dr. Sun Do Hwang for useful discussion. The datasets of the total confirmed cases of Covid-19 were retrieved from the Johns Hop- kins Center for Systems Science and Engineering Coronavirus Covid-19 Global Cases. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. 2019R1A6A1A03033215). [1] Fauci AS, Lane HC, Redfield RR. Covid-19 − Navigating the Uncharted. N. Engl. J. Med. 2020. doi: 10.1056/NEJMe2002387. [2] Cohen J, Kupferschmidt K. Countries test tactics in war against Covid-19. Science 2020; 367: 1287-1288. [3] Dong E, Du H, Gardner L. An interactive web-based dashboard to track Covid-19 in real time. Lancet Infect. Dis. 2020. https://doi.org/10.1016/S1473-3099(20)30120-1. [4] Normile D. Coronavirus cases have dropped sharply in South Korea. Whats the secret to its success? Science 2020. doi:10.1126/science.abb7566. [5] Anderson RM, Heesterbeek H, Klinkenberg D, Hollingsworth TD. How will country- based mitigation measures influence the course of the Covid-19 epidemic? Lancet 2020. https://doi.org/10.1016/S0140-6736(20)30567-5. 3 . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 30, 2020. ; https://doi.org/10.1101/2020.03.26.20044644doi: medRxiv preprint 2020-01-20 2020-02-03 2020-02-17 2020-03-02 2020-03-16 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 CKLQa SRXWK KRUHa IWaO\ USA IUaQ SSaQ GHUPaQ\ FUaQcH SZLW]HUOaQG UQLWHG KLQJGRP NHWKHUOaQGV AXVWULa TRWaO cRQILUPHG caVHV RI COVID-19 CaOHQGaU GaWH 05 1 0 1 5 2 0 2 5 3 0 3 5 4 0 1 10 100 CKLQa SRXWK KRUHa IWaO\ USA IUaQ SSaQ GHUPaQ\ FUaQcH SZLW]HUOaQG UQLWHG KLQJGRP NHWKHUOaQGV AXVWULa TRWaO cRQILUPHG caVHV (QRUPaOL]HG) Da\V VLQcH WKH 100WK cRQILUPHG caVH 2020-01-20 2020-02-03 2020-02-17 2020-03-02 2020-03-16 1 2 3 4 5 6 7 8 9 CKLQa SRXWK KRUHa IWaO\ USA IUaQ SSaQ GHUPaQ\ FUaQcH SZLW]HUOaQG UQLWHG KLQJGRP NHWKHUOaQGV AXVWULa DRXbOLQJ WLPH (Ga\) CaOHQGaU GaWH SRXWK KRUHa CKLQa IUaQ AXVWULa IWaO\ SSaLQ NHWKHUOaQGV FUaQcH SZLW]HUOaQG GHUPaQ\ UQLWHG KLQJGRP 0.00 0.05 0.10 0.15 DaLO\ LQcUHaVH RI GRXbOLQJ WLPH USA AB CD FIG. 1: A The total confirmed cases of Covid-19 for 12 countries as of March 23, retrieved from the Johns Hopkins CSSE, show the drastic growths. B The total cases normalized by N0 show the exponential growths of the Covid-19 total cases (N ). For reliable evaluations, N0 were chosen at N ≥ 100 (at or over the 100th case) and time was set to be 0 at N0 (see the same approach [2]; details of N and N0 in Appendix 1). C The doubling times taken from α(t) = t ln(2)/ ln(N/N0) demonstrate the time dependence of the doubling time (details of α(t) in Appendix 1). D The daily increases of the doubling times in 12 countries over the last 10 days (March 14 ∼ March 23) were estimated by the linear regression analyses with the software OriginPro (version 2019b). The error bars are the standard errors of the slopes (details of the regressions in Appendix 2). South Korea and China have the highest daily increases of the doubling times as ∼0.14 days per day, while India, Austria, Italy, Spain, Netherlands, France, and Switzerland have 0.10∼0.05 days per day, and finally Germany, UK, and USA have < 0.03 days per day. 4 . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 30, 2020. ; https://doi.org/10.1101/2020.03.26.20044644doi: medRxiv preprint 2020-01-20 2020-02-03 2020-02-17 2020-03-02 2020-03-16 0 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 China South Korea Italy USA Iran Span Germany France Switzerland United Kingdom Netherlands Austria Total confirmed cases of COVID-19 Calendar date 0 5 10 15 20 25 30 35 40 1 10 100 China South Korea Italy USA Iran Span Germany France Switzerland United Kingdom Netherlands Austria Total confirmed cases (normalized) Days since the 100th confirmed case 2020-01-20 2020-02-03 2020-02-17 2020-03-02 2020-03-16 1 2 3 4 5 6 7 8 9 China South Korea Italy USA Iran Span Germany France Switzerland United Kingdom Netherlands Austria Doubling time (day) Calendar date South Korea China Iran Austria Italy Spain Netherlands France Switzerland Germany United Kingdom 0.00 0.05 0.10 0.15 Daily increase of doubling time USA A B C D . CC-BY-NC-ND 4.0 International licenseIt is made available under a perpetuity. is the author/funder, who has granted medRxiv a license to display the preprint in(which was not certified by peer review)preprint The copyright holder for thisthis version posted March 30, 2020. ; https://doi.org/10.1101/2020.03.26.20044644doi: medRxiv preprint