Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2)
Identifieur interne : 001471 ( Pmc/Corpus ); précédent : 001470; suivant : 001472Substantial undocumented infection facilitates the rapid dissemination of novel coronavirus (SARS-CoV2)
Auteurs : Ruiyun Li ; Sen Pei ; Bin Chen ; Yimeng Song ; Tao Zhang ; Wan Yang ; Jeffrey ShamanSource :
- Science (New York, N.y.) [ 0036-8075 ] ; 2020.
Abstract
Estimation of the prevalence and contagiousness of undocumented novel coronavirus (SARS-CoV2) infections is critical for understanding the overall prevalence and pandemic potential of this disease. Here we use observations of reported infection within China, in conjunction with mobility data, a networked dynamic metapopulation model and Bayesian inference, to infer critical epidemiological characteristics associated with SARS-CoV2, including the fraction of undocumented infections and their contagiousness. We estimate 86% of all infections were undocumented (95% CI: [82%–90%]) prior to 23 January 2020 travel restrictions. Per person, the transmission rate of undocumented infections was 55% of documented infections ([46%–62%]), yet, due to their greater numbers, undocumented infections were the infection source for 79% of documented cases. These findings explain the rapid geographic spread of SARS-CoV2 and indicate containment of this virus will be particularly challenging.
Url:
DOI: 10.1126/science.abb3221
PubMed: 32179701
PubMed Central: 7164387
Links to Exploration step
PMC:7164387Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Substantial undocumented infection facilitates the rapid dissemination of
novel coronavirus (SARS-CoV2)</title><author><name sortKey="Li, Ruiyun" sort="Li, Ruiyun" uniqKey="Li R" first="Ruiyun" last="Li">Ruiyun Li</name><affiliation><nlm:aff id="aff1">MRC Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, School of Public Health, Faculty of Medicine, Imperial College London, London W2 1PG, UK.</nlm:aff></affiliation></author><author><name sortKey="Pei, Sen" sort="Pei, Sen" uniqKey="Pei S" first="Sen" last="Pei">Sen Pei</name><affiliation><nlm:aff id="aff2">Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.</nlm:aff></affiliation></author><author><name sortKey="Chen, Bin" sort="Chen, Bin" uniqKey="Chen B" first="Bin" last="Chen">Bin Chen</name><affiliation><nlm:aff id="aff3">Department of Land, Air and Water Resources, University of California, Davis, Davis, CA 95616, USA.</nlm:aff></affiliation></author><author><name sortKey="Song, Yimeng" sort="Song, Yimeng" uniqKey="Song Y" first="Yimeng" last="Song">Yimeng Song</name><affiliation><nlm:aff id="aff4">Department of Urban Planning and Design, The University of Hong Kong, Hong Kong.</nlm:aff></affiliation></author><author><name sortKey="Zhang, Tao" sort="Zhang, Tao" uniqKey="Zhang T" first="Tao" last="Zhang">Tao Zhang</name><affiliation><nlm:aff id="aff5">Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing 10084, P. R. China.</nlm:aff></affiliation></author><author><name sortKey="Yang, Wan" sort="Yang, Wan" uniqKey="Yang W" first="Wan" last="Yang">Wan Yang</name><affiliation><nlm:aff id="aff6">Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.</nlm:aff></affiliation></author><author><name sortKey="Shaman, Jeffrey" sort="Shaman, Jeffrey" uniqKey="Shaman J" first="Jeffrey" last="Shaman">Jeffrey Shaman</name><affiliation><nlm:aff id="aff2">Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">32179701</idno><idno type="pmc">7164387</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7164387</idno><idno type="RBID">PMC:7164387</idno><idno type="doi">10.1126/science.abb3221</idno><date when="2020">2020</date><idno type="wicri:Area/Pmc/Corpus">001471</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">001471</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Substantial undocumented infection facilitates the rapid dissemination of
novel coronavirus (SARS-CoV2)</title><author><name sortKey="Li, Ruiyun" sort="Li, Ruiyun" uniqKey="Li R" first="Ruiyun" last="Li">Ruiyun Li</name><affiliation><nlm:aff id="aff1">MRC Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, School of Public Health, Faculty of Medicine, Imperial College London, London W2 1PG, UK.</nlm:aff></affiliation></author><author><name sortKey="Pei, Sen" sort="Pei, Sen" uniqKey="Pei S" first="Sen" last="Pei">Sen Pei</name><affiliation><nlm:aff id="aff2">Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.</nlm:aff></affiliation></author><author><name sortKey="Chen, Bin" sort="Chen, Bin" uniqKey="Chen B" first="Bin" last="Chen">Bin Chen</name><affiliation><nlm:aff id="aff3">Department of Land, Air and Water Resources, University of California, Davis, Davis, CA 95616, USA.</nlm:aff></affiliation></author><author><name sortKey="Song, Yimeng" sort="Song, Yimeng" uniqKey="Song Y" first="Yimeng" last="Song">Yimeng Song</name><affiliation><nlm:aff id="aff4">Department of Urban Planning and Design, The University of Hong Kong, Hong Kong.</nlm:aff></affiliation></author><author><name sortKey="Zhang, Tao" sort="Zhang, Tao" uniqKey="Zhang T" first="Tao" last="Zhang">Tao Zhang</name><affiliation><nlm:aff id="aff5">Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing 10084, P. R. China.</nlm:aff></affiliation></author><author><name sortKey="Yang, Wan" sort="Yang, Wan" uniqKey="Yang W" first="Wan" last="Yang">Wan Yang</name><affiliation><nlm:aff id="aff6">Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.</nlm:aff></affiliation></author><author><name sortKey="Shaman, Jeffrey" sort="Shaman, Jeffrey" uniqKey="Shaman J" first="Jeffrey" last="Shaman">Jeffrey Shaman</name><affiliation><nlm:aff id="aff2">Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.</nlm:aff></affiliation></author></analytic><series><title level="j">Science (New York, N.y.)</title><idno type="ISSN">0036-8075</idno><idno type="eISSN">1095-9203</idno><imprint><date when="2020">2020</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>Estimation of the prevalence and contagiousness of undocumented novel coronavirus
(SARS-CoV2) infections is critical for understanding the overall prevalence and pandemic
potential of this disease. Here we use observations of reported infection within China, in
conjunction with mobility data, a networked dynamic metapopulation model and Bayesian
inference, to infer critical epidemiological characteristics associated with SARS-CoV2,
including the fraction of undocumented infections and their contagiousness. We estimate
86% of all infections were undocumented (95% CI: [82%–90%]) prior to 23 January
2020 travel restrictions. Per person, the transmission rate of undocumented infections was
55% of documented infections ([46%–62%]), yet, due to their greater numbers,
undocumented infections were the infection source for 79% of documented cases. These
findings explain the rapid geographic spread of SARS-CoV2 and indicate containment of this
virus will be particularly challenging.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Chan, J F" uniqKey="Chan J">J. F. Chan</name></author><author><name sortKey="Yuan, S" uniqKey="Yuan S">S. Yuan</name></author><author><name sortKey="Kok, K H" uniqKey="Kok K">K. H. Kok</name></author><author><name sortKey="To, K K" uniqKey="To K">K. K. To</name></author><author><name sortKey="Chu, H" uniqKey="Chu H">H. Chu</name></author><author><name sortKey="Yang, J" uniqKey="Yang J">J. Yang</name></author><author><name sortKey="Xing, F" uniqKey="Xing F">F. Xing</name></author><author><name sortKey="Liu, J" uniqKey="Liu J">J. Liu</name></author><author><name sortKey="Yip, C C" uniqKey="Yip C">C. C. Yip</name></author><author><name sortKey="Poon, R W" uniqKey="Poon R">R. W. Poon</name></author><author><name sortKey="Tsoi, H W" uniqKey="Tsoi H">H. W. Tsoi</name></author><author><name sortKey="Lo, S K" uniqKey="Lo S">S. K. Lo</name></author><author><name sortKey="Chan, K H" uniqKey="Chan K">K. H. Chan</name></author><author><name sortKey="Poon, V K" uniqKey="Poon V">V. K. Poon</name></author><author><name sortKey="Chan, W M" uniqKey="Chan W">W. M. Chan</name></author><author><name sortKey="Ip, J D" uniqKey="Ip J">J. D. Ip</name></author><author><name sortKey="Cai, J P" uniqKey="Cai J">J. P. Cai</name></author><author><name sortKey="Cheng, V C" uniqKey="Cheng V">V. C. Cheng</name></author><author><name sortKey="Chen, H" uniqKey="Chen H">H. Chen</name></author><author><name sortKey="Hui, C K" uniqKey="Hui C">C. K. Hui</name></author><author><name sortKey="Yuen, K Y" uniqKey="Yuen K">K. Y. Yuen</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wu, P" uniqKey="Wu P">P. Wu</name></author><author><name sortKey="Hao, X" uniqKey="Hao X">X. Hao</name></author><author><name sortKey="Lau, E H Y" uniqKey="Lau E">E. H. Y. Lau</name></author><author><name sortKey="Wong, J Y" uniqKey="Wong J">J. Y. Wong</name></author><author><name sortKey="Leung, K S X0a M" uniqKey="Leung K">K. S.
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<front><journal-meta><journal-id journal-id-type="nlm-ta">Science</journal-id><journal-id journal-id-type="iso-abbrev">Science</journal-id><journal-id journal-id-type="publisher-id">SCIENCE</journal-id><journal-title-group><journal-title>Science (New York, N.y.)</journal-title></journal-title-group><issn pub-type="ppub">0036-8075</issn><issn pub-type="epub">1095-9203</issn><publisher><publisher-name>American Association for the Advancement of Science</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">32179701</article-id><article-id pub-id-type="pmc">7164387</article-id><article-id pub-id-type="publisher-id">abb3221</article-id><article-id pub-id-type="doi">10.1126/science.abb3221</article-id><article-categories><subj-group subj-group-type="article-type"><subject>Research Article</subject></subj-group><subj-group subj-group-type="heading"><subject>Research Articles</subject></subj-group><subj-group subj-group-type="legacy-article-type"><subject>R-Articles</subject></subj-group><subj-group subj-group-type="field"><subject>Epidemiology</subject></subj-group></article-categories><title-group><article-title>Substantial undocumented infection facilitates the rapid dissemination of
novel coronavirus (SARS-CoV2)</article-title></title-group><contrib-group><contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0001-8927-9965</contrib-id><name><surname>Li</surname><given-names>Ruiyun</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref><xref ref-type="author-notes" rid="afn1">*</xref></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0002-7072-2995</contrib-id><name><surname>Pei</surname><given-names>Sen</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref><xref ref-type="author-notes" rid="afn1">*</xref><xref ref-type="corresp" rid="cor1">†</xref></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0003-3496-2876</contrib-id><name><surname>Chen</surname><given-names>Bin</given-names></name><xref ref-type="aff" rid="aff3"><sup>3</sup></xref><xref ref-type="author-notes" rid="afn1">*</xref></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0001-9558-1220</contrib-id><name><surname>Song</surname><given-names>Yimeng</given-names></name><xref ref-type="aff" rid="aff4"><sup>4</sup></xref></contrib><contrib contrib-type="author"><name><surname>Zhang</surname><given-names>Tao</given-names></name><xref ref-type="aff" rid="aff5"><sup>5</sup></xref></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0002-7555-9728</contrib-id><name><surname>Yang</surname><given-names>Wan</given-names></name><xref ref-type="award" rid="award587412"></xref><xref ref-type="aff" rid="aff6"><sup>6</sup></xref></contrib><contrib contrib-type="author"><contrib-id contrib-id-type="orcid" authenticated="true">https://orcid.org/0000-0002-7216-7809</contrib-id><name><surname>Shaman</surname><given-names>Jeffrey</given-names></name><xref ref-type="award" rid="award587411"></xref><xref ref-type="aff" rid="aff2"><sup>2</sup></xref><xref ref-type="corresp" rid="cor1">†</xref></contrib><aff id="aff1"><label>1</label>MRC Centre for Global Infectious Disease Analysis, Department of Infectious Disease Epidemiology, School of Public Health, Faculty of Medicine, Imperial College London, London W2 1PG, UK.</aff><aff id="aff2"><label>2</label>Department of Environmental Health Sciences, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.</aff><aff id="aff3"><label>3</label>Department of Land, Air and Water Resources, University of California, Davis, Davis, CA 95616, USA.</aff><aff id="aff4"><label>4</label>Department of Urban Planning and Design, The University of Hong Kong, Hong Kong.</aff><aff id="aff5"><label>5</label>Ministry of Education Key Laboratory for Earth System Modeling, Department of Earth System Science, Tsinghua University, Beijing 10084, P. R. China.</aff><aff id="aff6"><label>6</label>Department of Epidemiology, Mailman School of Public Health, Columbia University, New York, NY 10032, USA.</aff></contrib-group><author-notes><fn id="afn1" fn-type="equal"><label>*</label><p>These authors contributed equally to this work.</p></fn><corresp id="cor1"><label>†</label>Corresponding author. Email: <email xlink:href="sp3449@cumc.columbia.edu">sp3449@cumc.columbia.edu</email> (S.P.); <email xlink:href="jls106@cumc.columbia.edu">jls106@cumc.columbia.edu</email> (J.S.)</corresp></author-notes><pub-date pub-type="epub"><day>16</day><month>3</month><year>2020</year></pub-date><elocation-id>eabb3221</elocation-id><history><date date-type="received"><day>15</day><month>2</month><year>2020</year></date><date date-type="accepted"><day>12</day><month>3</month><year>2020</year></date></history><permissions><copyright-statement>Copyright © 2020, American Association for the Advancement of
Science</copyright-statement><copyright-year>2020</copyright-year><copyright-holder>American Association for the Advancement of Science</copyright-holder><license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by/4.0/"><ali:license_ref specific-use="vor" start_date="2020-03-04">https://creativecommons.org/licenses/by/4.0/</ali:license_ref><license-p>This open access article is distributed under <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License 4.0 (CC BY)</ext-link>.</license-p></license></permissions><abstract><p>Estimation of the prevalence and contagiousness of undocumented novel coronavirus
(SARS-CoV2) infections is critical for understanding the overall prevalence and pandemic
potential of this disease. Here we use observations of reported infection within China, in
conjunction with mobility data, a networked dynamic metapopulation model and Bayesian
inference, to infer critical epidemiological characteristics associated with SARS-CoV2,
including the fraction of undocumented infections and their contagiousness. We estimate
86% of all infections were undocumented (95% CI: [82%–90%]) prior to 23 January
2020 travel restrictions. Per person, the transmission rate of undocumented infections was
55% of documented infections ([46%–62%]), yet, due to their greater numbers,
undocumented infections were the infection source for 79% of documented cases. These
findings explain the rapid geographic spread of SARS-CoV2 and indicate containment of this
virus will be particularly challenging.</p></abstract><funding-group><award-group id="award587411"><funding-source><institution-wrap><institution-id institution-id-type="doi">http://dx.doi.org/10.13039/100000057</institution-id><institution>National Institute of General Medical Sciences</institution></institution-wrap></funding-source><award-id>GM110748</award-id></award-group><award-group id="award587412"><funding-source><institution-wrap><institution-id institution-id-type="doi">http://dx.doi.org/10.13039/100000060</institution-id><institution>National Institute of Allergy and Infectious Diseases</institution></institution-wrap></funding-source><award-id>AI145883</award-id></award-group></funding-group><custom-meta-group><custom-meta><meta-name>Number-color-figs</meta-name><meta-value>2</meta-value></custom-meta><custom-meta><meta-name>Number-figs</meta-name><meta-value>2</meta-value></custom-meta></custom-meta-group></article-meta></front><body><p> The novel coronavirus that emerged in Wuhan, China (SARS-CoV2) at the end of 2019 quickly
spread to all Chinese provinces and, as of 1 March 2020, to 58 other countries (<xref rid="R1" ref-type="bibr"><italic>1</italic></xref>, <xref rid="R2" ref-type="bibr"><italic>2</italic></xref>). Efforts to contain the virus are ongoing; however, given the
many uncertainties regarding pathogen transmissibility and virulence, the effectiveness of
these efforts is unknown.</p><p>The fraction of undocumented but infectious cases is a critical epidemiological
characteristic that modulates the pandemic potential of an emergent respiratory virus (<xref rid="R3" ref-type="bibr"><italic>3</italic></xref>–<xref rid="R6" ref-type="bibr"><italic>6</italic></xref>). These undocumented infections often experience mild, limited
or no symptoms and hence go unrecognized, and, depending on their contagiousness and numbers,
can expose a far greater portion of the population to virus than would otherwise occur. Here,
to assess the full epidemic potential of SARS-CoV2, we use a model-inference framework to
estimate the contagiousness and proportion of undocumented infections in China during the
weeks before and after the shutdown of travel in and out of Wuhan.</p><p>We developed a mathematical model that simulates the spatiotemporal dynamics of infections
among 375 Chinese cities (see supplementary materials). In the model, we divided infections
into two classes: (i) documented infected individuals with symptoms severe enough to be
confirmed, i.e., observed infections; and (ii) undocumented infected individuals. These two
classes of infection have separate rates of transmission: β, the transmission rate due
to documented infected individuals; and μβ, the transmission rate due to
undocumented individuals, which is β reduced by a factor μ.</p><p>Spatial spread of SARS-CoV2 across cities is captured by the daily number of people traveling
from city <italic>j</italic> to city <italic>i</italic> and a multiplicative factor.
Specifically, daily numbers of travelers between 375 Chinese cities during the Spring Festival
period (“Chunyun”) were derived from human mobility data collected by the
Tencent Location-based Service during the 2018 Chunyun period (1 February–12 March
2018) (<xref rid="R7" ref-type="bibr"><italic>7</italic></xref>). Chunyun is a period of 40
days—15 days before and 25 days after the Lunar New Year—during which there are
high rates of travel within China. To estimate human mobility during the 2020 Chunyun period,
which began 10 January, we aligned the 2018 Tencent data based on relative timing to the
Spring Festival. For example, we used mobility data from 1 February 2018 to represent human
movement on 10 January 2020, as these days were similarly distant from the Lunar New Year.
During the 2018 Chunyun, a total of 1.73 billion travel events were captured in the Tencent
data; whereas 2.97 billion trips are reported (<xref rid="R7" ref-type="bibr"><italic>7</italic></xref>). To compensate for underreporting and reconcile these two
numbers, a travel multiplicative factor, θ, which is greater than 1, is included (see
supplementary materials).</p><p>To infer SARS-CoV2 transmission dynamics during the early stage of the outbreak, we simulated
observations during 10–23 January 2020 (i.e., the period before the initiation of
travel restrictions, fig. S1) using an iterated filter-ensemble adjustment Kalman filter
(IF-EAKF) framework (<xref rid="R8" ref-type="bibr"><italic>8</italic></xref>–<xref rid="R10" ref-type="bibr"><italic>10</italic></xref>). With this combined model-inference
system, we estimated the trajectories of four model state variables
(<italic>S<sub>i</sub></italic>, <italic>E<sub>i</sub></italic>, <inline-formula><mml:math id="m1"><mml:mrow><mml:msubsup><mml:mi>I</mml:mi><mml:mi>i</mml:mi><mml:mi>r</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>, <inline-formula><mml:math id="m2"><mml:mrow><mml:msubsup><mml:mi>I</mml:mi><mml:mi>i</mml:mi><mml:mi>u</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>: the susceptible, exposed, documented infected, and
undocumented infected sub-populations in city <italic>i</italic>) for each of the 375 cities,
while simultaneously inferring six model parameters (<italic>Z</italic>, <italic>D</italic>,
μ, β, α, θ: the average latent period, the average duration of
infection, the transmission reduction factor for undocumented infections, the transmission
rate for documented infections; the fraction of documented infections, and the travel
multiplicative factor).</p><p>Details of model initialization, including the initial seeding of exposed and undocumented
infections, are provided in the supplementary materials. To account for delays in infection
confirmation, we also defined a time-to-event observation model using a Gamma distribution
(see supplementary materials). Specifically, for each new case in group
<inline-formula><mml:math id="m3"><mml:mrow><mml:msubsup><mml:mi>I</mml:mi><mml:mi>i</mml:mi><mml:mi>r</mml:mi></mml:msubsup></mml:mrow></mml:math></inline-formula>, a reporting delay <italic>t<sub>d</sub></italic> (in days) was
generated from a Gamma distribution with a mean value of <italic>T<sub>d</sub></italic>. In
fitting both synthetic and the observed outbreaks, we performed simulations with the
model-inference system using different fixed values of <italic>T<sub>d</sub></italic> (6 days
≤ <italic>T<sub>d</sub></italic> ≤ 10 days) and different maximum seeding,
<italic>Seed<sub>max</sub></italic> (1500 ≤ <italic>Seed<sub>max</sub></italic>≤ 2500) (see supplementary materials, fig. S2). The best fitting model-inference
posterior was identified by log-likelihood.</p><p>We first tested the model-inference framework versus alternate model forms and using
synthetic outbreaks generated by the model in free simulation. These tests verified the
ability of the model-inference framework to accurately estimate all six target model
parameters simultaneously (see supplementary methods and figs. S3 to S14). Indeed, the system
could identify a variety of parameter combinations and distinguish outbreaks generated with
high α and low μ from low α and high μ. This parameter
identifiability is facilitated by the assimilation of observed case data from multiple (375)
cities into the model-inference system and the incorporation of human movement in the
mathematical model structure (see supplementary methods and figs. S15 and S16).</p><p>We next applied the model-inference framework to the observed outbreak before the travel
restrictions of 23 January—a total of 801 documented cases throughout China, as
reported by 8 February 2020 (<xref rid="R1" ref-type="bibr"><italic>1</italic></xref>). <xref ref-type="fig" rid="F1">Figure 1, A to C</xref>, shows simulations of reported cases
generated using the best-fitting model parameter estimates. The distribution of these
stochastic simulations captures the range of observed cases well. In addition, the
best-fitting model captures the spread of infections with the novel coronavirus (COVID-19) to
other cities in China (fig. S17). Our median estimate of the effective reproductive number,
<italic>R<sub>e</sub></italic>—equivalent to the basic reproductive number
(<italic>R<sub>0</sub></italic>) at the beginning of the epidemic—is 2.38 (95% CI:
2.04−2.77), indicating a high capacity for sustained transmission of COVID-19 (<xref rid="T1" ref-type="table">Table 1</xref> and <xref ref-type="fig" rid="F1">Fig. 1D</xref>).
This finding aligns with other recent estimates of the reproductive number for this time
period (<xref rid="R6" ref-type="bibr"><italic>6</italic></xref>, <xref rid="R11" ref-type="bibr"><italic>11</italic></xref>–<xref rid="R15" ref-type="bibr"><italic>15</italic></xref>). In addition, the median estimates for the latent and
infectious periods are approximately 3.69 and 3.48 days, respectively. We also find that,
during 10–23 January, only 14% (95% CI: 10–18%) of total infections in China
were reported. This estimate reveals a very high rate of undocumented infections: 86%. This
finding is independently corroborated by the infection rate among foreign nationals evacuated
from Wuhan (see supplementary materials). These undocumented infections are estimated to have
been half as contagious per individual as reported infections (μ = 0.55; 95% CI:
0.46–0.62). Other model fittings made using alternate values of
<italic>T<sub>d</sub></italic> and <italic>Seed<sub>max</sub></italic> or different
distributional assumptions produced similar parameter estimates (figs. S18 to S22), as did
estimations made using an alternate model structure with separate average infection periods
for undocumented and documented infections (see supplementary methods, table S1). Further
sensitivity testing indicated that α and μ are uniquely identifiable given the
model structure and abundance of observations utilized (see supplementary methods and <xref ref-type="fig" rid="F1">Fig. 1, E and F</xref>). In particular, <xref ref-type="fig" rid="F1">Fig. 1F</xref> shows that the highest log-likelihood fittings are centered in the
95% CI estimates for α and μ and drop off with distance from the best fitting
solution (α= 0.14 and μ = 0.55).</p><fig id="F1" fig-type="figure" orientation="portrait" position="float"><label>Fig. 1</label><caption><title>Best-fit model and sensitivity analysis.</title><p>Simulation of daily reported cases in all cities (<bold>A</bold>), Wuhan city
(<bold>B</bold>) and Hubei province (<bold>C</bold>). The blue box and whiskers show the
median, interquartile range, and 95% credible intervals derived from 300 simulations using
the best-fit model (<xref rid="T1" ref-type="table">Table 1</xref>). The red x’s
are daily reported cases. The distribution of estimated <italic>R<sub>e</sub></italic> is
shown in (<bold>D</bold>). The impact of varying α and μ on
<italic>R<sub>e</sub></italic> with all other parameters held constant at <xref rid="T1" ref-type="table">Table 1</xref> mean values (<bold>E</bold>). The black solid
line indicates parameter combinations of (α,μ) yielding
<italic>R<sub>e</sub></italic> = 2.38. The estimated parameter combination α =
0.14 and μ = 0.55 is shown by the red x; the dashed box indicates the 95% credible
interval of that estimate. Log-likelihood for simulations with combinations of
(α,μ) and all other parameters held constant at <xref rid="T1" ref-type="table">Table 1</xref> mean values (<bold>F</bold>). For each parameter combination,
300 simulations were performed. The best-fit estimated parameter combination α =
0.14 and μ = 0.55 is shown by the red x (note that the x is plotted at the lower
left corner of its respective heat map pixel, i.e., the pixel with the highest log
likelihood); the dashed box indicates the 95% credible interval of that estimate.</p></caption><graphic xlink:href="abb3221-F1"></graphic></fig><table-wrap id="T1" orientation="portrait" position="float"><label>Table 1</label><caption><title>Best-fit model posterior estimates of key epidemiological parameters for simulation
with the full metapopulation model during 10–23 January 2020
(<italic>Seed<sub>max</sub></italic> = 2000, <italic>T<sub>d</sub></italic> = 9
days).</title></caption><table frame="hsides" rules="groups"><col width="58.98%" span="1"></col><col width="41.02%" span="1"></col><thead><tr><td valign="middle" align="left" scope="col" rowspan="1" colspan="1"><bold>Parameter</bold></td><td valign="middle" align="center" scope="col" rowspan="1" colspan="1"><bold>Median (95% CIs)</bold></td></tr></thead><tbody><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Transmission rate
(β<italic>,</italic> days<sup>−1</sup>)</td><td valign="middle" align="center" rowspan="1" colspan="1">1.12 (1.06, 1.19)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Relative transmission rate (μ)</td><td valign="middle" align="center" rowspan="1" colspan="1">0.55 (0.46, 0.62)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Latency period (<italic>Z,</italic>days)</td><td valign="middle" align="center" rowspan="1" colspan="1">3.69 (3.30, 3.96)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Infectious period (<italic>D,</italic>days)</td><td valign="middle" align="center" rowspan="1" colspan="1">3.47 (3.15, 3.73)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Reporting rate (α)</td><td valign="middle" align="center" rowspan="1" colspan="1">0.14 (0.10, 0.18)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Basic reproductive number
(<italic>R<sub>e</sub></italic>)</td><td valign="middle" align="center" rowspan="1" colspan="1">2.38 (2.03, 2.77)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Mobility factor (θ)</td><td valign="middle" align="center" rowspan="1" colspan="1">1.36 (1.27, 1.45)</td></tr></tbody></table></table-wrap><p>Using the best-fitting model (<xref rid="T1" ref-type="table">Table 1</xref> and <xref ref-type="fig" rid="F1">Fig. 1</xref>), we estimated 13,118 (95% CI: 2,974–23,435)
total new COVID-19 infections (documented and undocumented combined) during 10–23
January in Wuhan city. Further, 86.2% (95% CI: 81.5%–89.8%) of all infections were
infected from undocumented cases. Nationwide, the total number of infections during
10–23 January was 16,829 (95% CI: 3,797–30,271) with 86.2% (95% CI:
81.6%–89.8%) infected by undocumented cases.</p><p>To further examine the impact of contagious, undocumented COVID-19 infections on overall
transmission and reported case counts, we generated a set of hypothetical outbreaks using the
best-fitting parameter estimates but with μ = 0, i.e., the undocumented infections are
no longer contagious (<xref ref-type="fig" rid="F2">Fig. 2</xref>). We find that without
transmission from undocumented cases, reported infections during 10–23 January are
reduced 78.8% across all of China and 66.1% in Wuhan. Further, there are fewer cities with
more than 10 cumulative documented cases: only 1 city with more than 10 documented cases
versus the 10 observed by 23 January (<xref ref-type="fig" rid="F2">Fig. 2</xref>). This
finding indicates that contagious, undocumented infections facilitated the geographic spread
of SARS-CoV2 within China.</p><fig id="F2" fig-type="figure" orientation="portrait" position="float"><label>Fig. 2</label><caption><title>Impact of undocumented infections on the transmission of SARS-CoV2.</title><p>Simulations generated using the parameters reported in <xref rid="T1" ref-type="table">Table 1</xref> with μ = 0.55 (red) and μ = 0 (blue) showing daily
documented cases in all cities (<bold>A</bold>), daily documented cases in Wuhan city
(<bold>B</bold>) and the number of cities with ≥ 10<inline-formula><mml:math id="m4"><mml:mi> </mml:mi></mml:math></inline-formula>cumulative documented cases (<bold>C</bold>). The box and
whiskers show the median, interquartile range, and 95% credible intervals derived from 300
simulations.</p></caption><graphic xlink:href="abb3221-F2"></graphic></fig><p>We also modeled the transmission of COVID-19 in China after 23 January, when greater control
measures were effected. These control measures included travel restrictions imposed between
major cities and Wuhan; self-quarantine and contact precautions advocated by the government;
and more available rapid testing for infection confirmation (<xref rid="R11" ref-type="bibr"><italic>11</italic></xref>, <xref rid="R12" ref-type="bibr"><italic>12</italic></xref>).
These measures along with changes in medical care-seeking behavior due to increased awareness
of the virus and increased personal protective behavior (e.g., wearing of facemasks, social
distancing, self-isolation when sick), likely altered the epidemiological characteristics of
the outbreak after 23 January. To quantify these differences, we re-estimated the system
parameters using the model-inference framework and city-level daily cases reported between 24
January and 8 February. As inter-city mobility was restricted after 23 January, we tested two
altered travel scenarios: (i) scenario 1: a 98% reduction of travel in and out of Wuhan and an
80% reduction of travel between all other cities, as indicated by changes in the Baidu
Mobility Index (<xref rid="R16" ref-type="bibr"><italic>16</italic></xref>) (table S2); and
(ii) scenario 2: a complete stoppage of inter-city travel (i.e., θ to 0) (see
supplementary methods for more details).</p><p>The results of inference for the 24 January–8 February period are presented in <xref rid="T2" ref-type="table">Table 2</xref>, figs. S23 to S26, and table S3. As control
measures have continually shifted, we present estimates for both 24 January–3 February
(Period 1) and 24 January–8 February (Period 2). For both periods, the best-fitting
model for Scenario 1 had a reduced reporting delay, <italic>T<sub>d</sub></italic>, of 6 days
(vs. 10 days before 23 January), consistent with more rapid confirmation of infections.
Estimates of both the latency and infectious periods were similar to those made for
10–23 January; however, α, β, and <italic>R<sub>e</sub></italic> all
shifted considerably. The transmission rate of documented cases, β, dropped to 0.52
(95% CI: 0.39–0.71) during Period 1 and 0.35 (95% CI: 0.27–0.50) during Period
2, less than half the estimate prior to travel restrictions (<xref rid="T2" ref-type="table">Table 2</xref>). The fraction of all infections that were documented, α, was
estimated to be 0.65 (95% CI: 0.60–0.69), i.e., 65% of infections were documented
during Period 1, up from 14% prior to travel restrictions, and remained nearly the same for
Period 2. The reproductive number was 1.36 (95% CI: 1.14–1.63) during Period 1 and 0.99
(95% CI: 0.76–1.33) during Period 2, down from 2.38 prior to travel restrictions. While
the estimate for the relative transmission rate, μ, is lower than before 23 January,
the contagiousness of undocumented infections, represented by μβ, was
substantially reduced, possibly reflecting that only very mild, less contagious infections
remain undocumented or that individual protective behavior and contact precautions have proven
effective. Similar parameter estimates are derived under Scenario 2 (no travel at all) (table
S3). These inference results for both Period 1 and 2 should be interpreted with caution as
care-seeking behavior and control measures were continually in flux at these times.</p><table-wrap id="T2" orientation="portrait" position="float"><label>Table 2</label><caption><title>Best-fit model posterior estimates of key epidemiological parameters for simulation
of the model during 24 January–3 February and 24 January–8 February
(<italic>Seed<sub>max</sub></italic> = 2000 on 10 January,
<italic>T<sub>d</sub></italic> = 9 days before 24 January,
<italic>T<sub>d</sub></italic> = 6 days between 24 January and 8 February).</title><p>Travel to and from Wuhan is reduced by 98%, and other inter-city travel is reduced by
80%.</p></caption><table frame="hsides" rules="groups"><col width="38.08%" span="1"></col><col width="30.96%" span="1"></col><col width="30.96%" span="1"></col><thead><tr><td valign="middle" align="left" scope="col" rowspan="1" colspan="1"><bold>Parameter</bold></td><td valign="middle" align="center" scope="col" rowspan="1" colspan="1"><bold>24 January–3
February</bold><break></break><bold>[Median (95% CIs)]</bold></td><td valign="top" align="center" scope="col" rowspan="1" colspan="1"><bold>24 January–8
February</bold><break></break><bold>[Median (95% CIs)]</bold></td></tr></thead><tbody><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Transmission rate
(β<italic>,</italic> days<sup>−1</sup>)</td><td valign="top" align="center" rowspan="1" colspan="1">0.52 (0.42, 0.72)</td><td valign="top" align="center" rowspan="1" colspan="1">0.35 (0.28, 0.45)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Relative transmission rate (μ)</td><td valign="top" align="center" rowspan="1" colspan="1">0.50 (0.37, 0.69)</td><td valign="top" align="center" rowspan="1" colspan="1">0.43 (0.31, 0.61)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Latency period (<italic>Z,</italic>days)</td><td valign="top" align="center" rowspan="1" colspan="1">3.60 (3.41, 3.84)</td><td valign="top" align="center" rowspan="1" colspan="1">3.42 (3.30, 3.65)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Infectious period (<italic>D,</italic>days)</td><td valign="top" align="center" rowspan="1" colspan="1">3.14 (2.71, 3.72)</td><td valign="top" align="center" rowspan="1" colspan="1">3.31 (2.96, 3.88)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Reporting rate (α)</td><td valign="top" align="center" rowspan="1" colspan="1">0.65 (0.60, 0.69)</td><td valign="top" align="center" rowspan="1" colspan="1">0.69 (0.65, 0.72)</td></tr><tr><td valign="middle" align="left" scope="row" rowspan="1" colspan="1">Effective reproductive number
(<italic>R<sub>e</sub></italic>)</td><td valign="top" align="center" rowspan="1" colspan="1">1.34 (1.10, 1.67)</td><td valign="top" align="center" rowspan="1" colspan="1">0.98 (0.83, 1.16)</td></tr></tbody></table></table-wrap><p>Overall, our findings indicate that a large proportion of COVID-19 infections were
undocumented prior to the implementation of travel restrictions and other heightened control
measures in China on 23 January, and that a large proportion of the total force of infection
was mediated through these undocumented infections (<xref rid="T1" ref-type="table">Table
1</xref>). This high proportion of undocumented infections, many of whom were likely not
severely symptomatic, appears to have facilitated the rapid spread of the virus throughout
China. Indeed, suppression of the infectiousness of these undocumented cases in model
simulations reduces the total number of documented cases and the overall spread of SARS-CoV2
(<xref ref-type="fig" rid="F2">Fig. 2</xref>). In addition, the best-fitting model has a
reporting delay of 9 days from initial infectiousness to confirmation; in contrast line-list
data for the same 10–23 January period indicates an average 6.6 day delay from initial
manifestation of symptoms to confirmation (<xref rid="R17" ref-type="bibr"><italic>17</italic></xref>). This discrepancy suggests pre-symptomatic shedding may be
typical among documented infections. The relative timing of viremia and shedding onset and
peak versus symptom onset and peak has been shown to potentially affect outbreak control
success (<xref rid="R18" ref-type="bibr"><italic>18</italic></xref>).</p><p>Our findings also indicate that a radical increase in the identification and isolation of
currently undocumented infections would be needed to fully control SARS-CoV2. Increased news
coverage and awareness of the virus in the general population have already likely prompted
increased rates of seeking medical care for respiratory symptoms. In addition, awareness among
healthcare providers, public health officials and the availability of viral identification
assays suggest that capacity for identifying previously missed infections has increased.
Further, general population and government response efforts have increased the use of face
masks, restricted travel, delayed school reopening and isolated suspected persons, all of
which could additionally slow the spread of SARS-CoV2.</p><p>Combined, these measures are expected to increase reporting rates, reduce the proportion of
undocumented infections, and decrease the growth and spread of infection. Indeed, estimation
of the epidemiological characteristics of the outbreak after 23 January in China, indicate
that government control efforts and population awareness have reduced the rate of spread of
the virus (i.e., lower β, μβ, <italic>R<sub>e</sub></italic>), increased
the reporting rate, and lessened the burden on already over-extended healthcare systems.</p><p>Importantly, the situation on the ground in China is changing day-to-day. New travel
restrictions and control measures are being imposed on new populations in different cities,
and these rapidly varying effects make certain estimation of the epidemiological
characteristics for the outbreak difficult. Further, reporting inaccuracies and changing
care-seeking behavior add another level of uncertainty to our estimations. While the data and
findings presented here indicate that travel restrictions and control measures have reduced
SARS-CoV2 transmission considerably, whether these controls are sufficient for reducing
<italic>R<sub>e</sub></italic> below 1 for the length of time needed to eliminate the
disease locally and prevent a rebound outbreak once control measures are relaxed is unclear.
Further, similar control measures and travel restrictions would have to be implemented outside
China to prevent reintroduction of the virus.</p><p>The results for 10–23 January 2020 delineate the characteristics of the SARS-CoV2
moving through a developed society, China, without major restrictions or control. These
findings provide a baseline assessment of the fraction of undocumented infections and their
relative infectiousness for such an environment. However, differences in control activity,
viral surveillance and testing, and case definition and reporting would likely impact rates of
infection documentation. Thus, the key findings, that 86% of infections went undocumented and
that, per person, these undocumented infections were 55% as contagious as documented
infections, could shift in other countries with different control, surveillance and reporting
practices.</p><p>Our findings underscore the seriousness and pandemic potential of SARS-CoV2. The 2009 H1N1
pandemic influenza virus also caused many mild cases, quickly spread globally, and eventually
became endemic. Presently, there are four, endemic, coronavirus strains currently circulating
in human populations (229E, HKU1, NL63, OC43). If the novel coronavirus follows the pattern of
2009 H1N1 pandemic influenza, it will also spread globally and become a fifth endemic
coronavirus within the human population.</p></body><back><ack><title>Acknowledgments</title><p><bold>Funding:</bold> This work was supported by US NIH grants GM110748 and AI145883. The
content is solely the responsibility of the authors and does not necessarily represent the
official views of the National Institute of General Medical Sciences, the National Institute
for Allergy and Infectious Diseases, or the National Institutes of Health. <bold>Author
contributions:</bold> R.L., S.P., B.C., W.Y. and J.S. conceived the study. R.L., B.C.,
Y.S. and T.Z. curated data. S.P. performed the analysis. R.L., S.P., W.Y. and J.S. wrote the
first draft of the manuscript. B.C, Y.S. and T.Z. reviewed and edited the manuscript.
<bold>Competing interests:</bold> J.S. and Columbia University disclose partial ownership
of SK Analytics. J.S. also reports receiving consulting fees from Merck and BNI. All other
authors declare no competing interests. <bold>Data and materials availability:</bold> All
code and data are available in the supplementary materials and posted online at <ext-link ext-link-type="uri" xlink:href="https://github.com/SenPei-CU/COVID-19">https://github.com/SenPei-CU/COVID-19</ext-link> and (<xref rid="R19" ref-type="bibr"><italic>19</italic></xref>).</p></ack><sec sec-type="ppv-message"><p><bold>Correction (25 March 2020):</bold> Li <italic>et al</italic>. have identified an
error in the code in lines 44 to 49 of SEIR.m and in equation 4 of the supplementary
materials. This produces a very small error in the denominator population size in some of
the model terms. The authors have rerun the model and find that the parameter estimates are
almost identical and the conclusions are unchanged. Corrections have been made in Tables 1
and 2, the supplementary materials (including tables S1 and S3), and the code. </p></sec><app-group><app><title>Supplementary Materials</title><supplementary-material content-type="local-data"><p><ext-link ext-link-type="uri" xlink:href="https://science.sciencemag.org/cgi/content/full/science.abb3221/DC1">science.sciencemag.org/cgi/content/full/science.abb3221/DC1</ext-link></p><p>Materials and Methods</p><p>Figs. S1 to S26</p><p>Tables S1 to S3</p><p>References (<xref rid="R20" ref-type="bibr"><italic>20</italic></xref>–<xref rid="R37" ref-type="bibr"><italic>37</italic></xref>)</p><p>MDAR Reproducibility Checklist</p><p>Data S1</p></supplementary-material><supplementary-material content-type="local-data" id="S1"><media xlink:href="abb3221_Li_SM_rev.pdf"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S2"><media xlink:href="abb3221_MDAR_checklist.pdf"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S3"><media xlink:href="cities.mat"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S4"><media xlink:href="incidence.mat"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S5"><media xlink:href="inference.m"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S6"><media xlink:href="initialize.m"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S7"><media xlink:href="M.mat"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S8"><media xlink:href="pop.mat"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S9"><media xlink:href="SEIR.m"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S10"><media xlink:href="city_coordinates.csv"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S11"><media xlink:href="Incidence.csv"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S12"><media xlink:href="Mobility.csv"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material><supplementary-material content-type="local-data" id="S13"><media xlink:href="pop.csv"><caption><p>Click here for additional data file.</p></caption></media></supplementary-material></app></app-group><ref-list><title>References and Notes</title><ref id="R1"><label>1</label><mixed-citation publication-type="web">National Health Commission of the People’s
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