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High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2

High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2 RESEARCH High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2 1 1 Steven Sanche , Yen Ting Lin , Chonggang Xu, Ethan Romero-Severson, Nick Hengartner, Ruian Ke of the limited amount of data available. In addi- Severe acute respiratory syndrome coronavirus 2 is the tion, unavailability of diagnostic reagents early causative agent of the ongoing coronavirus disease pan- in the outbreak, changes in surveillance intensity demic. Initial estimates of the early dynamics of the out- and case definitions, and overwhelmed health - break in Wuhan, China, suggested a doubling time of the care systems confound estimates of the growth number of infected persons of 6–7 days and a basic re- productive number (R ) of 2.2–2.7. We collected exten- of the outbreak based on data. Initial estimates of sive individual case reports across China and estimated the exponential growth rate of the outbreak were key epidemiologic parameters, including the incubation 0.1–0.14/day (a doubling time of 6–7 days), and a period (4.2 days). We then designed 2 mathematical basic reproductive number (R ; defined as the av - modeling approaches to infer the outbreak dynamics in erage number of secondary cases attributable to Wuhan by using high-resolution domestic travel and in- infection by an index case after that case is intro- fection data. Results show that the doubling time early duced into a susceptible population) ranged from in the epidemic in Wuhan was 2.3–3.3 days. Assuming 2.2 to 2.7 (1,3–5). These estimates were based on 2 a serial interval of 6–9 days, we calculated a median R broad strategies. First, Li et al. used very early case value of 5.7 (95% CI 3.8–8.9). We further show that ac- count data in Wuhan before January 4 (1). Howev- tive surveillance, contact tracing, quarantine, and early er, case count data can be confounded by reservoir strong social distancing efforts are needed to stop trans - mission of the virus. spillover events, stochasticities in the initial phase of the outbreak, and low surveillance intensity. evere acute respiratory syndrome coronavirus The epidemic curve based on symptom onset after S2 (SARS-CoV-2) is the etiologic agent of the cur- January 4 showed a very different growth rate (6). rent rapidly growing outbreak of coronavirus disease Second, inference was performed by using inter- (COVID-19), originating from the city of Wuhan, Hu- national flight data and infected persons reported bei Province, China (1). Initially, 41 cases of “pneu- outside of China (3–5). Because of the low numbers monia of unknown etiology” were reported to the of persons traveling abroad compared with the to- World Health Organization by the Wuhan Munici- tal population size in Wuhan, this approach leads pal Health Committee at the end of December 2019 to substantial uncertainties (7,8). Inferences based (2). On January 8, 2020, the pathogen was identified on a low number of observations are prone to mea- (1), and human-to-human transmission was reported surement error when data are incomplete or model soon after. By January 21, most provinces of China assumptions are not fully justified; both conditions had reported COVID-19 cases. By March 16, the out- are common challenges associated with rapid and break had led to >170,000 total confirmed cases and early outbreak analyses of a new pathogen. >6,500 deaths globally. In a period of 3 months, an We collected an expanded set of case reports outbreak of apparent idiopathic pneumonia had be- across China on the basis of publicly available in- come the COVID-19 pandemic. formation, estimated key epidemiologic parameters, Studying dynamics of a newly emerged and and provided a new estimate of the early epidemic rapidly growing infectious disease outbreak, such growth rate and R in Wuhan. Our approaches are as COVID-19, is important but challenging because based on integration of high-resolution domestic travel data and early infection data reported in prov- Author affiliation: Los Alamos National Laboratory, Los Alamos, inces other than Hubei to infer outbreak dynamics in New Mexico, USA These first authors contributed equally to this article. DOI: https://doi.org/10.3201/eid2607.200282 1470 Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 High Contagiousness and Rapid Spread of SARS-CoV-2 Data Wuhan. They are designed to be less sensitive to bi- ases and confounding factors in the data and model Individual Case Reports assumptions. Without directly using case confirma - We collected publicly available reports of 140 con- tion data in Wuhan, we avoid the potential biases in firmed COVID-19 cases (mostly outside Hubei Prov - reporting and case confirmation in Wuhan, whereas ince). These reports were published by the Chinese because of the high level of domestic travel before Centers for Disease Control and Prevention (China the Lunar New Year in China, inference based on CDC) and provincial health commissions; accession these data minimizes uncertainties and risk for po- dates were January 15–30, 2020 (Appendix 1 Table tential misspecifications and biases in data and mod - 1, https://wwwnc.cdc.gov/EID/article/26/7/20- el assumptions. 0282-App1.xlsx). Many of the individual reports were also published on the China CDC official Methods website (http://www.chinacdc.cn/jkzt/crb/zl/ szkb_11803) and the English version of the China Methodologic Overview CDC weekly bulletin (http://weekly.chinacdc.cn/ We developed 2 modeling approaches to infer the news/TrackingtheEpidemic.htm). These reports growth rate of the outbreak in Wuhan from data include demographic information as well as epide- from provinces other than Hubei. In the first model, miologic information, including potential periods the first arrival model, we computed the likelihood of infection, and dates of symptom onset, hospital- of the arrival times of the first known cases in prov - ization, and case confirmation. Most of the health inces outside of Hubei as a function of the exponen- commissions in provinces and special municipalities tial growing population of infected persons in Wuhan documented and published detailed information of before late January. This calculation involved using the first or the first few patients with confirmed CO - domestic travel data to compute the probability that VID-19. As a result, a unique feature of this dataset an infected person traveled from Wuhan to a given includes case reports of many of the first or the first province as a function of the unknown actual number few persons who were confirmed to have SARS- of infected persons in Wuhan and the probability that CoV-2 virus infection in each province, where dates they traveled. The timings of the arrivals of the first of departure from Wuhan were available. infected persons in different provinces would reflect the rate of the epidemic growth in Wuhan. Travel Data In the second model, the case count model, we ac- We used the Baidu Migration server (https://qianxi. counted for the detection of additional persons who baidu.com) to estimate the number of daily travelers were infected in Wuhan and received their diagnoses in and out of Wuhan (Appendix 1 Table 2). in other provinces and explicitly modeled those per- The server is an online platform summarizing sons by using a hybrid deterministic–stochastic SEIR mobile phone travel data hosted by Baidu Huiyan (susceptible-exposed-infectious-recovered) model. (https://huiyan.baidu.com). We then fitted this model to new daily case count data reported outside Hubei Province during the pe- Calculations of R and Effect of Intervention Strategies riod before substantial transmission occurred outside We considered realistic distributions for the latent of the province. and infectious periods to calculate R . We described By using data collected outside Hubei Prov- the methods we used to calculate R and the effect of ince, we minimized the effect of changes in surveil- intervention strategies on the outbreak (Appendix 2, lance intensity. By the time cases were confirmed https://wwwnc.cdc.gov/EID/article/26/7/20-0282- in provinces outside Hubei, all of the provinces of App2.pdf). China had access to diagnostic kits and were engag- ing in active surveillance of travelers out of Wuhan Results (e.g., using temperatures detectors and digital data to identify infected persons [ 9]) as the outbreak un - Estimating Distributions of Epidemiologic Parameters folded. Furthermore, the healthcare systems out- We first translated reports from documents or news side Hubei were not yet overwhelmed with cases reports published daily from the China CDC web- and were actively searching for the first positive site and official websites of health commissions case, leading to much lower bias in the reporting across provinces and special municipalities in China in each province compared with the time series of during January 15–30, 2020. Altogether, we collected confirmed cases in Wuhan. Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 1471 RESEARCH 137 individual case reports from China and 3 addi- change in durations might only reflect changes in the tional case reports from outside of China (Appendix rest of China (rather than in Hubei). We also found 1 Table 1). that the time from initial hospital admittance to dis- By using this dataset, we estimated the basic pa- charge was 11.5 days (95% CI 8.0–17.3 days) (Figure 1, rameter distributions of durations from initial expo- panel C) and from initial hospital admittance to death sure to symptom onset to hospitalization to discharge was 11.2 days (95% CI 8.7–14.9 days) (Figure 1, panel or death. Our estimate of the time from initial expo- D). The time from symptom onset to death was esti- sure to symptom onset (i.e., the incubation period) mated to be 16.1 days (95% CI 13.1–20.2 days). is 4.2 days (95% CI 3.5–5.1 days) (Figure 1, panel A), based on 24 case reports. This estimated duration is Estimating the Growth Rate of the Outbreak in generally consistent with a recent report by Guan et Wuhan in January 2020 al. (10) showing that the median incubation period is Moving from empirical estimates of basic epidemio- 4 days. Our estimate is ≈1 day shorter than 2 previ- logic parameters to an understanding of the early ous estimates (1,11). One potential caveat of our es- growth rates of COVID-19 requires model-based in- timation is that because most of the case reports we ference and data. We first collected real-time travel collected were from the first few persons detected data during the epidemic by using the Baidu Migra- in each province, this estimation might be biased to- tion server, which provides real-time travel patterns ward patients with more severe symptoms if they are in China based on mobile-phone positioning services more likely to be detected. (Figure 2, panel A; Appendix 1 Methods, Table 2). The time from symptom onset to hospitalization We estimated that, before the January 23 lockdown showed evidence of time dependence (Figure 1, panel of the city, ≈40,000–140,000 people in Wuhan traveled B; Appendix 2 Figure 1). Before January 18, the time to destinations outside Hubei Province each day (Fig- from symptom onset to hospitalization was 5.5 days ure 2, panel B). The extensive travel before the Lunar (95% CI 4.6–6.6 days), whereas after January 18, the New Year was probably an important driver of the duration shortened significantly to 1.5 days (95% CI spread of COVID-19 in China. 1.2–1.9 days) (p<0.001 by Mann–Whitney U test). The We then integrated spatiotemporal domestic change in the distribution coincides with news re- travel data to infer the outbreak dynamics in Wuhan ports of potential human-to-human transmission and by using two mathematical approaches (Appendix upgrading of emergency response level to Level 1 by 2; conceptual framework depicted in Figure 3, panel the China CDC. The emerging consensus about the A). The first-arrival model uses a unique feature of risk for COVID-19 probably led to substantial behav- our case report dataset whereby the dates of depar- ior changes among symptomatic persons, in terms of ture from Wuhan for many of the first persons who seeking more timely medical care during this period. were confirmed with SARS-CoV-2 infection in each However, because most of the individual reports province were known (Appendix 1 Table 1). We as- were collected in provinces other than Hubei, the sumed an exponential growth for the total infected Figure 1. Epidemiologic characteristics of early dynamics of coronavirus disease outbreak in China. Distributions of key epidemiologic parameters: durations from infection to symptom onset (A), from symptom onset to hospitalization (B), from hospitalization to discharge (C), and from hospitalization to death (D). Filled circles and bars on x-axes denote the estimated means and 95% CIs. 1472 Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 High Contagiousness and Rapid Spread of SARS-CoV-2 Figure 2. Extremely high level of travel from Wuhan, Hubei Province, to other provinces during January 2020, as estimated by using high-resolution and real-time travel data, China. A) A modified snapshot of the Baidu Migration online server interface showing the human migration pattern out of Wuhan (red dot) on January 19, 2020. Thickness of curved white lines denotes the size of the traveler population to each province. The names of most of the provinces are shown in white. B) Estimated daily population sizes of travelers from Wuhan to other provinces. r(t–t ) population I* in Wuhan, I*(t) = e , where I* in- We further estimated that the total infected cludes infected persons who are asymptomatic or population size in Wuhan was ≈4,100 (95% CI 2,423– symptomatic, r is the exponential growth rate, and t 6,178) on January 18 (Appendix 2 Figure 3), which is the theoretical time of the exponential growth initi- is consistent with a recently posted estimate (7). The ation, so that I (t ) = 1 in the deterministic model. We estimated number of infected persons was ≈18,700 call t a “theoretical” time in the sense that it should (95% CI 7,147–38,663) on January 23 (i.e., the date not be interpreted as the time of first infection in a when Wuhan started its lockdown). We projected population. We should expect that t is later than the that without any control measures, the infected pop- date of the first infection because multiple spillover ulation would be ≈233,400 (95% CI 38,757–778,278) events from the animal reservoir might be needed by the end of January. to establish sustained transmission and stochasticity An alternative model, the case count approach, might play a large role in initial dynamics before the used daily new case counts of persons who had onset of exponential growth (12–14). COVID-19 diagnosed in other provinces but who We used travel data for each of the provinces (Ap- had been in Hubei Province within 14 days of be- pendix 1 Table 3) and the earliest times that an infected coming symptomatic. This model uses data be- person arrived in a province, across a total of 26 prov- yond the first appearance of an infected person inces (Figure 3, panel B), to infer r and t (Appendix 2). from Wuhan but also accounts for the stochastic Model predictions of arrival times in the 26 provinces nature of the process by using a hybrid model. In fitted the actual data well (Appendix 2 Figure 2). The this model, the infected population in Wuhan was growth rate r is estimated to be 0.29/day (95% CI 0.21– described with a deterministic model, whereas the 0.37/day), corresponding to a doubling time of 2.4 days infected persons who traveled from Wuhan to oth- (95% CI 1.9–3.3 days). t is estimated to be December 20, er provinces were tracked with a stochastic SEIR 2019 (95% CI December 11–26). As we show later, there (susceptible-exposed-infectious-recovered) model exist larger uncertainties in the estimation of t . (12). We restricted the data to the period of January Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 1473 RESEARCH Figure 3. Estimates of the exponential growth rate and the date of exponential growth initiation of the coronavirus disease outbreak in China based on 2 different approaches. A) Schematic illustrating the export of infected persons from Wuhan. Travelers (dots) are assumed to be random samples from the total population (whole pie). Because of the growth of the infected population (orange pie) and the shrinking size of the total population in Wuhan over time, probability of infected persons traveling to other provinces increases (orange dots). B) The dates of documented first arrivals of infected persons in 26 provinces. C) Best fit of the case count model to daily counts of new cases (including only imported cases) in provinces other than Hubei. Error bars indicate SDs. 19–26, when new cases reported were mostly in- our data in general do not support this hypothesis fections imported from Wuhan (i.e., indicative of on the basis of corrected Akaike Information crite- the dynamics in Wuhan). The transitions of the in- rion scores (Appendix 1 Table 4). However, if the fected persons from symptom onset to hospitaliza- intensity of surveillance outside Hubei Province in- tion and then to case confirmation were assumed creased over the period of January, we would pre- to follow the distributions inferred from the case dict a lower growth rate than the estimate we just report data (Appendix 2). Simulation of the model described. For the worst-case scenario considered, using best-fit parameters showed that the model we estimated the growth rate of the outbreak to be described the observed case counts over time well 0.21/day (Appendix 2). (Figure 3, panel C). The estimated theoretical time (t ) is December 16, 2019 (95% CI December 12–21), Other Evidence of a High Growth Rate of the and the exponential growth rate is 0.30/day (95% Outbreak in Wuhan CI 0.26–0.34/day). These estimates are consistent In addition to using 2 modeling approaches, we with estimates in the first arrival approach (Figure looked for other evidence of a high outbreak growth 4; Appendix 2 Figure 4). rate to cross-validate our estimations. We found that In both models, we assumed perfect detection the time series of reported deaths in Hubei, which is (i.e., of infected cases outside of Hubei Province). less subject to the biases of the confirmed case counts, However, a certain fraction of cases probably was is simply not consistent with a growth rate of 0.1/ not reported. To investigate the robustness of our day (Appendix 2 Figure 5). As the infected popula- estimates, we performed extensive sensitivity anal- tion grows, the number of death cases will grow at yses to test 23 different scenarios of surveillance in- the same rate but with a delayed onset corresponding tensity (Appendix 2). First, we tested the assump- to the time from infection to death. Fitting a simple tion that a constant fraction of infected persons exponential growth model to the number of reported (e.g., persons with mild or no symptoms) (15) were deaths in Hubei during late January 2020 yields an not detected. We found that under this assumption, estimate of 0.22–0.27/day, which is within the 95% CI t would be earlier than our estimate but the estima- of the estimation we previously described. tion of the growth rate remained the same (Appen- Overall, these analyses suggest that although dix 1 Table 4). Second, we tested the assumption there exist uncertainties depending on the level of that the intensity of surveillance increases over the surveillance, the exponential growth rate of the out- period of data collection, although this scenario is break is probably 0.21–0.3/day. This estimation is less likely because of the intensive surveillance im- much higher than previous reports, in which the plemented outside Hubei Province. We found that growth rate was estimated to be 0.1–0.14/day (1,3–5). 1474 Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 High Contagiousness and Rapid Spread of SARS-CoV-2 Estimating R The basic reproductive number, R , is dependent on the exponential growth rate of an outbreak, as well as additional factors such as the latent period (the time from infection to infectiousness) and the infectious period (16,17), both of which cannot be estimated directly from the data. Following the approach by Wearing and Rohani (16), we found that with a high growth rate of the outbreak, R is in general high and the longer the latent and the infectious periods, the higher the estimated R (Appendix 2 Figure 6). To derive realistic values of R , we used previous estimates of serial intervals for COVID-19. The serial interval is estimated to be ≈7–8 days based on data collected early in the outbreak in Wuhan (1). More re- cent data collected in Shenzhen Province, China, sug- gests that the serial interval is dependent on the time Figure 4. Marginalized likelihoods of growth rate (r) for 2 inference approaches to estimates the exponential growth rate of the to hospital isolation (Q. Bi et al., unpub. data, https:// coronavirus disease outbreak in China. doi.org/10.1101/2020.03.03.20028423). When infect- ed persons are isolated after 5 days of symptoms (a probable scenario for the early outbreak in Wuhan, et al., unpub data. https://doi.org/10.1101/2020.03. where the public was not aware of the virus and few 05.20030502); thus, we believe that a mean serial in- interventions were implemented), the serial interval terval shorter than 6 days is unlikely during the early is estimated to be 8 days (Q. Bi et al., unpub. data). outbreak in Wuhan, where infected persons were not Thus, these results suggest a serial interval of 7–8 rapidly hospitalized. days. With this serial interval, we sampled latent and infectious periods within wide biologically plausible Implications for Intervention Strategies ranges (Appendix 2) and estimated the median R to The R values we estimated have important implica- 0 0 be 5.8 (95% CI 4.4–7.7) (Figure 5, panel A). To include tions for predicting the effects of pharmaceutical and a wider range of serial interval (i.e., 6–9 days) (Figure nonpharmaceutical interventions. For example, the 5, panel A; Appendix 2 Figure 6), given the uncertain- threshold for combined vaccine efficacy and herd im - ties in these estimations, we estimated that the me- munity needed for disease extinction is calculated as dian of estimated R is 5.7 (95% CI of 3.8–8.9) (Figure 1 – 1/R . At R = 2.2, this threshold is only 55%. But at 0 0 0 5, panel B). The estimated R can be lower if the serial R = 5.7, this threshold rises to 82% (i.e., >82% of the 0 0 interval is shorter. However, recent studies reported population has to be immune, through either vaccina- that persons can be infectious for a long period, such tion or prior infection, to achieve herd immunity to as 1–3 weeks after symptom onset (18; R. Woelfel stop transmission). Figure 5. Estimation of the basic reproductive number (R ), derived by integrating uncertainties in parameter values, during the coronavirus disease outbreak in China. A) Changes in R based on different growth rates and serial intervals. Each dot represents a calculation with mean latent period (range 2.2–6 days) and mean infectious periods (range 4–14 days). Only those estimates falling within the range of serial intervals of interests were plotted. B) Histogram summarizing the estimated R of all dots in panel A (i.e., serial interval ranges of 6–9 days). The median R is 5.7 (95% CI 3.8–8.9). Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 1475 RESEARCH days), a time dependent duration from symptom on- set to hospitalization (changing from 5.5 days in early January to 1.5 days in late January outside Hubei Province), and the time from symptom onset to death (16.1 days). By using 2 distinct approaches, we esti- mated the growth rate of the early outbreak in Wu- han to be 0.21–0.30 per day (a doubling time of 2.3–3.3 days), suggesting a much faster rate of spread than initially measured. This finding would have impor - tant implications for forecasting epidemic trajectories and the effect on healthcare systems as well as for evaluating the effectiveness of intervention strategies. We found R is likely to be 5.7 given our current state of knowledge, with a broad 95% CI (3.8–8.9). Among many factors, the lack of awareness of this new pathogen and the Lunar New Year travel and Figure 6. Levels of minimum efforts of intervention strategies needed to control the spread of severe acute respiratory syndrome gathering in early and mid-January 2020 might or coronavirus 2, (i.e. reducing the reproductive number to <1), during might not play a role in the high R . A recent study the coronavirus disease outbreak in China. Strategies considered based on structural analysis of the virus particles sug- were quarantine of infected persons and persons who had contact gests SARS-CoV-2 has a much higher affinity to the with them (x-axis) and population-level efforts to reduce overall receptor needed for cell entry than the 2003 SARS contact rates (y-axis). Percentages denote the percentages of transmissions driven by infected persons that were not detected by virus (21), providing a molecular basis for the high surveillance as a result of asymptomatic infection, mild-to-moderate infectiousness of SARS-CoV-2. illness or low surveillance intensity. How contagious SARS-CoV-2 is in other coun- tries remains to be seen. Given the rapid rate of We then evaluated the effectiveness for nonphar- spread as seen in current outbreaks in Europe, we maceutical interventions, such as contact tracing, quar- need to be aware of the difficulty of controlling SARS- antine, and social distancing, by using the framework CoV-2 once it establishes sustained human-to-human by Lipsitch et al. (19) (Appendix 2). We extended the transmission in a new population (20). Our results framework to consider a fraction of transmission occur- suggest that a combination of control measures, in- ring from infected persons who would not be identified cluding early and active surveillance, quarantine, and by surveillance and can transmit effectively (15). This especially strong social distancing efforts, are needed fraction is determined by the fraction of actual asymp- to slow down or stop the spread of the virus. If these tomatic persons and the extent of surveillance efforts to measures are not implemented early and strongly, identify these persons and persons with mild-to-moder- the virus has the potential to spread rapidly and in- ate symptoms. Results show that quarantine and contact fect a large fraction of the population, overwhelming tracing of symptomatic persons can be effective when healthcare systems. Fortunately, the decline in newly the fraction of unidentified persons is low. However, confirmed cases in China and South Korea in March when 20% of transmission is driven by unidentified 2020 and the stably low incidences in Taiwan, Hong infected persons, high levels of social distancing efforts Kong, and Singapore strongly suggest that the spread will be needed to contain the virus (Figure 6), highlight- of the virus can be contained with early and appropri- ing the importance of early and effective surveillance, ate measures. contact tracing, and quarantine. Future field, laboratory, and modeling studies aimed to address the unknowns, Acknowledgments such as the fraction of asymptomatic persons, the extent We thank Alan Perelson, Christiaan van Dorp, and Ruy of their transmissibility depending on symptom sever- Ribeiro for suggestions and critical reading of the ity, the time when persons become infectious, and the manuscript and Weili Yin for help with collecting and existence of superspreaders are needed to accurately translating documents from provincial health predict the impact of various control strategies (20). commission websites. Discussion S.S. and R.K. received funding from the Defense Advanced In this study, we estimated several basic epidemio- Research Projects Agency (grant no. HR0011938513) and logic parameters, including the incubation period (4.2 the Laboratory Directed Research and Development Rapid 1476 Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 High Contagiousness and Rapid Spread of SARS-CoV-2 medicine/sph/ide/gida-fellowships/Imperial-College- Response Program through the Center for Nonlinear COVID19-update-epidemic-size-22-01-2020.pdf Studies at Los Alamos National Laboratory. C.X. received 8. Imai N, Dorigatti I, Cori A, Riley S, Ferguson NM. funding from Laboratory Directed Research and Estimating the potential total number of novel coronavirus Development Program. E.R.S. received funding from the cases in Wuhan City, China [cited 2020 Feb 2]. https://www. imperial.ac.uk/media/imperial-college/medicine/sph/ide/ National Institutes of Health (grant no. R01AI135946). gida-fellowships/2019-nCoV-outbreak-report-17-01-2020.pdf The funders had no role in study design, data collection 9. Hongyang L. Railway corporation using big data to trace and analysis, decision to publish, or preparation of potential virus carrier. ChinaDailyNews [cited 2020 Feb 1]. the manuscript. https://www.chinadaily.com.cn/a/202001/30/ WS5e329ca2a310128217273b89.html Author contributions: R.K. and N.H. conceived the project; 10. Guan WJ, Ni ZY, Hu Y, Liang WH, Ou CQ, He JX, et al.; R.K. collected data; S.S., Y.T.L., C.X., and R.K. performed China Medical Treatment Expert Group for Covid-19. Clinical characteristics of coronavirus disease 2019 in analyses; S.S., Y.T.L., E.R.S., N.H., and R.K. wrote and China. N Engl J Med. 2020 Feb 28 [Epub ahead of print]. edited the manuscript. https://doi.org/10.1056/NEJMoa2002032 11. Lauer SA, Grantz KH, Bi Q, Jones FK, Zheng Q, Meredith Authors declare no competing interests. All data are HR, et al. The incubation period of coronavirus disease 2019 available in the main text and in Appendices 1 and 2. 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Science. 2020;367:1260–3. in China [in Chinese]. Zhonghua Liu Xing Bing Xue Za Zhi. https://doi.org/10.1126/science.abb2507 2020;41:145–51. 7. Imai N, Dorigatti I, Cori A, Donnelly C, Riley S. Ferguson. Address for correspondence: Ruian Ke, T-6 Theoretical Biology Report 2: estimating the potential total number of novel and Biophysics, Mailstop K710, Los Alamos National Laboratory, coronavirus cases in Wuhan City, China [cited 2020 Feb 2]. https://www.imperial.ac.uk/media/imperial-college/ NM 87544, USA; email: rke@lanl.gov Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 1477 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Emerging Infectious Diseases Pubmed Central

High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2

Emerging Infectious Diseases , Volume 26 (7) – Jul 1, 2020

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10.3201/eid2607.200282
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Abstract

RESEARCH High Contagiousness and Rapid Spread of Severe Acute Respiratory Syndrome Coronavirus 2 1 1 Steven Sanche , Yen Ting Lin , Chonggang Xu, Ethan Romero-Severson, Nick Hengartner, Ruian Ke of the limited amount of data available. In addi- Severe acute respiratory syndrome coronavirus 2 is the tion, unavailability of diagnostic reagents early causative agent of the ongoing coronavirus disease pan- in the outbreak, changes in surveillance intensity demic. Initial estimates of the early dynamics of the out- and case definitions, and overwhelmed health - break in Wuhan, China, suggested a doubling time of the care systems confound estimates of the growth number of infected persons of 6–7 days and a basic re- productive number (R ) of 2.2–2.7. We collected exten- of the outbreak based on data. Initial estimates of sive individual case reports across China and estimated the exponential growth rate of the outbreak were key epidemiologic parameters, including the incubation 0.1–0.14/day (a doubling time of 6–7 days), and a period (4.2 days). We then designed 2 mathematical basic reproductive number (R ; defined as the av - modeling approaches to infer the outbreak dynamics in erage number of secondary cases attributable to Wuhan by using high-resolution domestic travel and in- infection by an index case after that case is intro- fection data. Results show that the doubling time early duced into a susceptible population) ranged from in the epidemic in Wuhan was 2.3–3.3 days. Assuming 2.2 to 2.7 (1,3–5). These estimates were based on 2 a serial interval of 6–9 days, we calculated a median R broad strategies. First, Li et al. used very early case value of 5.7 (95% CI 3.8–8.9). We further show that ac- count data in Wuhan before January 4 (1). Howev- tive surveillance, contact tracing, quarantine, and early er, case count data can be confounded by reservoir strong social distancing efforts are needed to stop trans - mission of the virus. spillover events, stochasticities in the initial phase of the outbreak, and low surveillance intensity. evere acute respiratory syndrome coronavirus The epidemic curve based on symptom onset after S2 (SARS-CoV-2) is the etiologic agent of the cur- January 4 showed a very different growth rate (6). rent rapidly growing outbreak of coronavirus disease Second, inference was performed by using inter- (COVID-19), originating from the city of Wuhan, Hu- national flight data and infected persons reported bei Province, China (1). Initially, 41 cases of “pneu- outside of China (3–5). Because of the low numbers monia of unknown etiology” were reported to the of persons traveling abroad compared with the to- World Health Organization by the Wuhan Munici- tal population size in Wuhan, this approach leads pal Health Committee at the end of December 2019 to substantial uncertainties (7,8). Inferences based (2). On January 8, 2020, the pathogen was identified on a low number of observations are prone to mea- (1), and human-to-human transmission was reported surement error when data are incomplete or model soon after. By January 21, most provinces of China assumptions are not fully justified; both conditions had reported COVID-19 cases. By March 16, the out- are common challenges associated with rapid and break had led to >170,000 total confirmed cases and early outbreak analyses of a new pathogen. >6,500 deaths globally. In a period of 3 months, an We collected an expanded set of case reports outbreak of apparent idiopathic pneumonia had be- across China on the basis of publicly available in- come the COVID-19 pandemic. formation, estimated key epidemiologic parameters, Studying dynamics of a newly emerged and and provided a new estimate of the early epidemic rapidly growing infectious disease outbreak, such growth rate and R in Wuhan. Our approaches are as COVID-19, is important but challenging because based on integration of high-resolution domestic travel data and early infection data reported in prov- Author affiliation: Los Alamos National Laboratory, Los Alamos, inces other than Hubei to infer outbreak dynamics in New Mexico, USA These first authors contributed equally to this article. DOI: https://doi.org/10.3201/eid2607.200282 1470 Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 High Contagiousness and Rapid Spread of SARS-CoV-2 Data Wuhan. They are designed to be less sensitive to bi- ases and confounding factors in the data and model Individual Case Reports assumptions. Without directly using case confirma - We collected publicly available reports of 140 con- tion data in Wuhan, we avoid the potential biases in firmed COVID-19 cases (mostly outside Hubei Prov - reporting and case confirmation in Wuhan, whereas ince). These reports were published by the Chinese because of the high level of domestic travel before Centers for Disease Control and Prevention (China the Lunar New Year in China, inference based on CDC) and provincial health commissions; accession these data minimizes uncertainties and risk for po- dates were January 15–30, 2020 (Appendix 1 Table tential misspecifications and biases in data and mod - 1, https://wwwnc.cdc.gov/EID/article/26/7/20- el assumptions. 0282-App1.xlsx). Many of the individual reports were also published on the China CDC official Methods website (http://www.chinacdc.cn/jkzt/crb/zl/ szkb_11803) and the English version of the China Methodologic Overview CDC weekly bulletin (http://weekly.chinacdc.cn/ We developed 2 modeling approaches to infer the news/TrackingtheEpidemic.htm). These reports growth rate of the outbreak in Wuhan from data include demographic information as well as epide- from provinces other than Hubei. In the first model, miologic information, including potential periods the first arrival model, we computed the likelihood of infection, and dates of symptom onset, hospital- of the arrival times of the first known cases in prov - ization, and case confirmation. Most of the health inces outside of Hubei as a function of the exponen- commissions in provinces and special municipalities tial growing population of infected persons in Wuhan documented and published detailed information of before late January. This calculation involved using the first or the first few patients with confirmed CO - domestic travel data to compute the probability that VID-19. As a result, a unique feature of this dataset an infected person traveled from Wuhan to a given includes case reports of many of the first or the first province as a function of the unknown actual number few persons who were confirmed to have SARS- of infected persons in Wuhan and the probability that CoV-2 virus infection in each province, where dates they traveled. The timings of the arrivals of the first of departure from Wuhan were available. infected persons in different provinces would reflect the rate of the epidemic growth in Wuhan. Travel Data In the second model, the case count model, we ac- We used the Baidu Migration server (https://qianxi. counted for the detection of additional persons who baidu.com) to estimate the number of daily travelers were infected in Wuhan and received their diagnoses in and out of Wuhan (Appendix 1 Table 2). in other provinces and explicitly modeled those per- The server is an online platform summarizing sons by using a hybrid deterministic–stochastic SEIR mobile phone travel data hosted by Baidu Huiyan (susceptible-exposed-infectious-recovered) model. (https://huiyan.baidu.com). We then fitted this model to new daily case count data reported outside Hubei Province during the pe- Calculations of R and Effect of Intervention Strategies riod before substantial transmission occurred outside We considered realistic distributions for the latent of the province. and infectious periods to calculate R . We described By using data collected outside Hubei Prov- the methods we used to calculate R and the effect of ince, we minimized the effect of changes in surveil- intervention strategies on the outbreak (Appendix 2, lance intensity. By the time cases were confirmed https://wwwnc.cdc.gov/EID/article/26/7/20-0282- in provinces outside Hubei, all of the provinces of App2.pdf). China had access to diagnostic kits and were engag- ing in active surveillance of travelers out of Wuhan Results (e.g., using temperatures detectors and digital data to identify infected persons [ 9]) as the outbreak un - Estimating Distributions of Epidemiologic Parameters folded. Furthermore, the healthcare systems out- We first translated reports from documents or news side Hubei were not yet overwhelmed with cases reports published daily from the China CDC web- and were actively searching for the first positive site and official websites of health commissions case, leading to much lower bias in the reporting across provinces and special municipalities in China in each province compared with the time series of during January 15–30, 2020. Altogether, we collected confirmed cases in Wuhan. Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 1471 RESEARCH 137 individual case reports from China and 3 addi- change in durations might only reflect changes in the tional case reports from outside of China (Appendix rest of China (rather than in Hubei). We also found 1 Table 1). that the time from initial hospital admittance to dis- By using this dataset, we estimated the basic pa- charge was 11.5 days (95% CI 8.0–17.3 days) (Figure 1, rameter distributions of durations from initial expo- panel C) and from initial hospital admittance to death sure to symptom onset to hospitalization to discharge was 11.2 days (95% CI 8.7–14.9 days) (Figure 1, panel or death. Our estimate of the time from initial expo- D). The time from symptom onset to death was esti- sure to symptom onset (i.e., the incubation period) mated to be 16.1 days (95% CI 13.1–20.2 days). is 4.2 days (95% CI 3.5–5.1 days) (Figure 1, panel A), based on 24 case reports. This estimated duration is Estimating the Growth Rate of the Outbreak in generally consistent with a recent report by Guan et Wuhan in January 2020 al. (10) showing that the median incubation period is Moving from empirical estimates of basic epidemio- 4 days. Our estimate is ≈1 day shorter than 2 previ- logic parameters to an understanding of the early ous estimates (1,11). One potential caveat of our es- growth rates of COVID-19 requires model-based in- timation is that because most of the case reports we ference and data. We first collected real-time travel collected were from the first few persons detected data during the epidemic by using the Baidu Migra- in each province, this estimation might be biased to- tion server, which provides real-time travel patterns ward patients with more severe symptoms if they are in China based on mobile-phone positioning services more likely to be detected. (Figure 2, panel A; Appendix 1 Methods, Table 2). The time from symptom onset to hospitalization We estimated that, before the January 23 lockdown showed evidence of time dependence (Figure 1, panel of the city, ≈40,000–140,000 people in Wuhan traveled B; Appendix 2 Figure 1). Before January 18, the time to destinations outside Hubei Province each day (Fig- from symptom onset to hospitalization was 5.5 days ure 2, panel B). The extensive travel before the Lunar (95% CI 4.6–6.6 days), whereas after January 18, the New Year was probably an important driver of the duration shortened significantly to 1.5 days (95% CI spread of COVID-19 in China. 1.2–1.9 days) (p<0.001 by Mann–Whitney U test). The We then integrated spatiotemporal domestic change in the distribution coincides with news re- travel data to infer the outbreak dynamics in Wuhan ports of potential human-to-human transmission and by using two mathematical approaches (Appendix upgrading of emergency response level to Level 1 by 2; conceptual framework depicted in Figure 3, panel the China CDC. The emerging consensus about the A). The first-arrival model uses a unique feature of risk for COVID-19 probably led to substantial behav- our case report dataset whereby the dates of depar- ior changes among symptomatic persons, in terms of ture from Wuhan for many of the first persons who seeking more timely medical care during this period. were confirmed with SARS-CoV-2 infection in each However, because most of the individual reports province were known (Appendix 1 Table 1). We as- were collected in provinces other than Hubei, the sumed an exponential growth for the total infected Figure 1. Epidemiologic characteristics of early dynamics of coronavirus disease outbreak in China. Distributions of key epidemiologic parameters: durations from infection to symptom onset (A), from symptom onset to hospitalization (B), from hospitalization to discharge (C), and from hospitalization to death (D). Filled circles and bars on x-axes denote the estimated means and 95% CIs. 1472 Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 High Contagiousness and Rapid Spread of SARS-CoV-2 Figure 2. Extremely high level of travel from Wuhan, Hubei Province, to other provinces during January 2020, as estimated by using high-resolution and real-time travel data, China. A) A modified snapshot of the Baidu Migration online server interface showing the human migration pattern out of Wuhan (red dot) on January 19, 2020. Thickness of curved white lines denotes the size of the traveler population to each province. The names of most of the provinces are shown in white. B) Estimated daily population sizes of travelers from Wuhan to other provinces. r(t–t ) population I* in Wuhan, I*(t) = e , where I* in- We further estimated that the total infected cludes infected persons who are asymptomatic or population size in Wuhan was ≈4,100 (95% CI 2,423– symptomatic, r is the exponential growth rate, and t 6,178) on January 18 (Appendix 2 Figure 3), which is the theoretical time of the exponential growth initi- is consistent with a recently posted estimate (7). The ation, so that I (t ) = 1 in the deterministic model. We estimated number of infected persons was ≈18,700 call t a “theoretical” time in the sense that it should (95% CI 7,147–38,663) on January 23 (i.e., the date not be interpreted as the time of first infection in a when Wuhan started its lockdown). We projected population. We should expect that t is later than the that without any control measures, the infected pop- date of the first infection because multiple spillover ulation would be ≈233,400 (95% CI 38,757–778,278) events from the animal reservoir might be needed by the end of January. to establish sustained transmission and stochasticity An alternative model, the case count approach, might play a large role in initial dynamics before the used daily new case counts of persons who had onset of exponential growth (12–14). COVID-19 diagnosed in other provinces but who We used travel data for each of the provinces (Ap- had been in Hubei Province within 14 days of be- pendix 1 Table 3) and the earliest times that an infected coming symptomatic. This model uses data be- person arrived in a province, across a total of 26 prov- yond the first appearance of an infected person inces (Figure 3, panel B), to infer r and t (Appendix 2). from Wuhan but also accounts for the stochastic Model predictions of arrival times in the 26 provinces nature of the process by using a hybrid model. In fitted the actual data well (Appendix 2 Figure 2). The this model, the infected population in Wuhan was growth rate r is estimated to be 0.29/day (95% CI 0.21– described with a deterministic model, whereas the 0.37/day), corresponding to a doubling time of 2.4 days infected persons who traveled from Wuhan to oth- (95% CI 1.9–3.3 days). t is estimated to be December 20, er provinces were tracked with a stochastic SEIR 2019 (95% CI December 11–26). As we show later, there (susceptible-exposed-infectious-recovered) model exist larger uncertainties in the estimation of t . (12). We restricted the data to the period of January Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 1473 RESEARCH Figure 3. Estimates of the exponential growth rate and the date of exponential growth initiation of the coronavirus disease outbreak in China based on 2 different approaches. A) Schematic illustrating the export of infected persons from Wuhan. Travelers (dots) are assumed to be random samples from the total population (whole pie). Because of the growth of the infected population (orange pie) and the shrinking size of the total population in Wuhan over time, probability of infected persons traveling to other provinces increases (orange dots). B) The dates of documented first arrivals of infected persons in 26 provinces. C) Best fit of the case count model to daily counts of new cases (including only imported cases) in provinces other than Hubei. Error bars indicate SDs. 19–26, when new cases reported were mostly in- our data in general do not support this hypothesis fections imported from Wuhan (i.e., indicative of on the basis of corrected Akaike Information crite- the dynamics in Wuhan). The transitions of the in- rion scores (Appendix 1 Table 4). However, if the fected persons from symptom onset to hospitaliza- intensity of surveillance outside Hubei Province in- tion and then to case confirmation were assumed creased over the period of January, we would pre- to follow the distributions inferred from the case dict a lower growth rate than the estimate we just report data (Appendix 2). Simulation of the model described. For the worst-case scenario considered, using best-fit parameters showed that the model we estimated the growth rate of the outbreak to be described the observed case counts over time well 0.21/day (Appendix 2). (Figure 3, panel C). The estimated theoretical time (t ) is December 16, 2019 (95% CI December 12–21), Other Evidence of a High Growth Rate of the and the exponential growth rate is 0.30/day (95% Outbreak in Wuhan CI 0.26–0.34/day). These estimates are consistent In addition to using 2 modeling approaches, we with estimates in the first arrival approach (Figure looked for other evidence of a high outbreak growth 4; Appendix 2 Figure 4). rate to cross-validate our estimations. We found that In both models, we assumed perfect detection the time series of reported deaths in Hubei, which is (i.e., of infected cases outside of Hubei Province). less subject to the biases of the confirmed case counts, However, a certain fraction of cases probably was is simply not consistent with a growth rate of 0.1/ not reported. To investigate the robustness of our day (Appendix 2 Figure 5). As the infected popula- estimates, we performed extensive sensitivity anal- tion grows, the number of death cases will grow at yses to test 23 different scenarios of surveillance in- the same rate but with a delayed onset corresponding tensity (Appendix 2). First, we tested the assump- to the time from infection to death. Fitting a simple tion that a constant fraction of infected persons exponential growth model to the number of reported (e.g., persons with mild or no symptoms) (15) were deaths in Hubei during late January 2020 yields an not detected. We found that under this assumption, estimate of 0.22–0.27/day, which is within the 95% CI t would be earlier than our estimate but the estima- of the estimation we previously described. tion of the growth rate remained the same (Appen- Overall, these analyses suggest that although dix 1 Table 4). Second, we tested the assumption there exist uncertainties depending on the level of that the intensity of surveillance increases over the surveillance, the exponential growth rate of the out- period of data collection, although this scenario is break is probably 0.21–0.3/day. This estimation is less likely because of the intensive surveillance im- much higher than previous reports, in which the plemented outside Hubei Province. We found that growth rate was estimated to be 0.1–0.14/day (1,3–5). 1474 Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 High Contagiousness and Rapid Spread of SARS-CoV-2 Estimating R The basic reproductive number, R , is dependent on the exponential growth rate of an outbreak, as well as additional factors such as the latent period (the time from infection to infectiousness) and the infectious period (16,17), both of which cannot be estimated directly from the data. Following the approach by Wearing and Rohani (16), we found that with a high growth rate of the outbreak, R is in general high and the longer the latent and the infectious periods, the higher the estimated R (Appendix 2 Figure 6). To derive realistic values of R , we used previous estimates of serial intervals for COVID-19. The serial interval is estimated to be ≈7–8 days based on data collected early in the outbreak in Wuhan (1). More re- cent data collected in Shenzhen Province, China, sug- gests that the serial interval is dependent on the time Figure 4. Marginalized likelihoods of growth rate (r) for 2 inference approaches to estimates the exponential growth rate of the to hospital isolation (Q. Bi et al., unpub. data, https:// coronavirus disease outbreak in China. doi.org/10.1101/2020.03.03.20028423). When infect- ed persons are isolated after 5 days of symptoms (a probable scenario for the early outbreak in Wuhan, et al., unpub data. https://doi.org/10.1101/2020.03. where the public was not aware of the virus and few 05.20030502); thus, we believe that a mean serial in- interventions were implemented), the serial interval terval shorter than 6 days is unlikely during the early is estimated to be 8 days (Q. Bi et al., unpub. data). outbreak in Wuhan, where infected persons were not Thus, these results suggest a serial interval of 7–8 rapidly hospitalized. days. With this serial interval, we sampled latent and infectious periods within wide biologically plausible Implications for Intervention Strategies ranges (Appendix 2) and estimated the median R to The R values we estimated have important implica- 0 0 be 5.8 (95% CI 4.4–7.7) (Figure 5, panel A). To include tions for predicting the effects of pharmaceutical and a wider range of serial interval (i.e., 6–9 days) (Figure nonpharmaceutical interventions. For example, the 5, panel A; Appendix 2 Figure 6), given the uncertain- threshold for combined vaccine efficacy and herd im - ties in these estimations, we estimated that the me- munity needed for disease extinction is calculated as dian of estimated R is 5.7 (95% CI of 3.8–8.9) (Figure 1 – 1/R . At R = 2.2, this threshold is only 55%. But at 0 0 0 5, panel B). The estimated R can be lower if the serial R = 5.7, this threshold rises to 82% (i.e., >82% of the 0 0 interval is shorter. However, recent studies reported population has to be immune, through either vaccina- that persons can be infectious for a long period, such tion or prior infection, to achieve herd immunity to as 1–3 weeks after symptom onset (18; R. Woelfel stop transmission). Figure 5. Estimation of the basic reproductive number (R ), derived by integrating uncertainties in parameter values, during the coronavirus disease outbreak in China. A) Changes in R based on different growth rates and serial intervals. Each dot represents a calculation with mean latent period (range 2.2–6 days) and mean infectious periods (range 4–14 days). Only those estimates falling within the range of serial intervals of interests were plotted. B) Histogram summarizing the estimated R of all dots in panel A (i.e., serial interval ranges of 6–9 days). The median R is 5.7 (95% CI 3.8–8.9). Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 1475 RESEARCH days), a time dependent duration from symptom on- set to hospitalization (changing from 5.5 days in early January to 1.5 days in late January outside Hubei Province), and the time from symptom onset to death (16.1 days). By using 2 distinct approaches, we esti- mated the growth rate of the early outbreak in Wu- han to be 0.21–0.30 per day (a doubling time of 2.3–3.3 days), suggesting a much faster rate of spread than initially measured. This finding would have impor - tant implications for forecasting epidemic trajectories and the effect on healthcare systems as well as for evaluating the effectiveness of intervention strategies. We found R is likely to be 5.7 given our current state of knowledge, with a broad 95% CI (3.8–8.9). Among many factors, the lack of awareness of this new pathogen and the Lunar New Year travel and Figure 6. Levels of minimum efforts of intervention strategies needed to control the spread of severe acute respiratory syndrome gathering in early and mid-January 2020 might or coronavirus 2, (i.e. reducing the reproductive number to <1), during might not play a role in the high R . A recent study the coronavirus disease outbreak in China. Strategies considered based on structural analysis of the virus particles sug- were quarantine of infected persons and persons who had contact gests SARS-CoV-2 has a much higher affinity to the with them (x-axis) and population-level efforts to reduce overall receptor needed for cell entry than the 2003 SARS contact rates (y-axis). Percentages denote the percentages of transmissions driven by infected persons that were not detected by virus (21), providing a molecular basis for the high surveillance as a result of asymptomatic infection, mild-to-moderate infectiousness of SARS-CoV-2. illness or low surveillance intensity. How contagious SARS-CoV-2 is in other coun- tries remains to be seen. Given the rapid rate of We then evaluated the effectiveness for nonphar- spread as seen in current outbreaks in Europe, we maceutical interventions, such as contact tracing, quar- need to be aware of the difficulty of controlling SARS- antine, and social distancing, by using the framework CoV-2 once it establishes sustained human-to-human by Lipsitch et al. (19) (Appendix 2). We extended the transmission in a new population (20). Our results framework to consider a fraction of transmission occur- suggest that a combination of control measures, in- ring from infected persons who would not be identified cluding early and active surveillance, quarantine, and by surveillance and can transmit effectively (15). This especially strong social distancing efforts, are needed fraction is determined by the fraction of actual asymp- to slow down or stop the spread of the virus. If these tomatic persons and the extent of surveillance efforts to measures are not implemented early and strongly, identify these persons and persons with mild-to-moder- the virus has the potential to spread rapidly and in- ate symptoms. Results show that quarantine and contact fect a large fraction of the population, overwhelming tracing of symptomatic persons can be effective when healthcare systems. Fortunately, the decline in newly the fraction of unidentified persons is low. However, confirmed cases in China and South Korea in March when 20% of transmission is driven by unidentified 2020 and the stably low incidences in Taiwan, Hong infected persons, high levels of social distancing efforts Kong, and Singapore strongly suggest that the spread will be needed to contain the virus (Figure 6), highlight- of the virus can be contained with early and appropri- ing the importance of early and effective surveillance, ate measures. contact tracing, and quarantine. Future field, laboratory, and modeling studies aimed to address the unknowns, Acknowledgments such as the fraction of asymptomatic persons, the extent We thank Alan Perelson, Christiaan van Dorp, and Ruy of their transmissibility depending on symptom sever- Ribeiro for suggestions and critical reading of the ity, the time when persons become infectious, and the manuscript and Weili Yin for help with collecting and existence of superspreaders are needed to accurately translating documents from provincial health predict the impact of various control strategies (20). commission websites. Discussion S.S. and R.K. received funding from the Defense Advanced In this study, we estimated several basic epidemio- Research Projects Agency (grant no. HR0011938513) and logic parameters, including the incubation period (4.2 the Laboratory Directed Research and Development Rapid 1476 Emerging Infectious Diseases • www.cdc.gov/eid • Vol. 26, No. 7, July 2020 High Contagiousness and Rapid Spread of SARS-CoV-2 medicine/sph/ide/gida-fellowships/Imperial-College- Response Program through the Center for Nonlinear COVID19-update-epidemic-size-22-01-2020.pdf Studies at Los Alamos National Laboratory. C.X. received 8. Imai N, Dorigatti I, Cori A, Riley S, Ferguson NM. funding from Laboratory Directed Research and Estimating the potential total number of novel coronavirus Development Program. E.R.S. received funding from the cases in Wuhan City, China [cited 2020 Feb 2]. https://www. imperial.ac.uk/media/imperial-college/medicine/sph/ide/ National Institutes of Health (grant no. R01AI135946). gida-fellowships/2019-nCoV-outbreak-report-17-01-2020.pdf The funders had no role in study design, data collection 9. Hongyang L. Railway corporation using big data to trace and analysis, decision to publish, or preparation of potential virus carrier. ChinaDailyNews [cited 2020 Feb 1]. the manuscript. https://www.chinadaily.com.cn/a/202001/30/ WS5e329ca2a310128217273b89.html Author contributions: R.K. and N.H. conceived the project; 10. Guan WJ, Ni ZY, Hu Y, Liang WH, Ou CQ, He JX, et al.; R.K. collected data; S.S., Y.T.L., C.X., and R.K. performed China Medical Treatment Expert Group for Covid-19. Clinical characteristics of coronavirus disease 2019 in analyses; S.S., Y.T.L., E.R.S., N.H., and R.K. wrote and China. N Engl J Med. 2020 Feb 28 [Epub ahead of print]. edited the manuscript. https://doi.org/10.1056/NEJMoa2002032 11. Lauer SA, Grantz KH, Bi Q, Jones FK, Zheng Q, Meredith Authors declare no competing interests. All data are HR, et al. The incubation period of coronavirus disease 2019 available in the main text and in Appendices 1 and 2. (COVID-19) from publicly reported confirmed cases: estimation and application. Ann Intern Med. 2020 Mar 10 [Epub ahead of print]. https://doi.org/10.7326/M20-0504 About the Author 12. Anderson RM, May RM. Infectious diseases of humans: Dr. Sanche is a postdoctoral research associate at Los dynamics and control. Oxford Science Publications. Oxford: Oxford University Press; 1991. p. 768. Alamos National Laboratory, Los Alamos, New Mexico, 13. Lloyd-Smith JO, Schreiber SJ, Kopp PE, Getz WM. USA. His primary research interest lies in complex disease Superspreading and the effect of individual variation on dynamics inferred from data science and mathematical disease emergence. Nature. 2005;438:355–9. https://doi.org/ modeling. Dr. Lin is also a postdoctoral research associate 10.1038/nature04153 14. Romero-Severson EO, Ribeiro RM, Castro M. Noise is not at Los Alamos National Laboratory. 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Emerging Infectious DiseasesPubmed Central

Published: Jul 1, 2020

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