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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak</title><author><name sortKey="Zhao, Shi" sort="Zhao, Shi" uniqKey="Zhao S" first="Shi" last="Zhao">Shi Zhao</name><affiliation><nlm:aff id="aff0005">JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China</nlm:aff></affiliation><affiliation><nlm:aff id="aff0010">Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China</nlm:aff></affiliation></author><author><name sortKey="Lin, Qianyin" sort="Lin, Qianyin" uniqKey="Lin Q" first="Qianyin" last="Lin">Qianyin Lin</name><affiliation><nlm:aff id="aff0015">Michigan Institute for Data Science, University of Michigan, Ann Arbor, MI, USA</nlm:aff></affiliation></author><author><name sortKey="Ran, Jinjun" sort="Ran, Jinjun" uniqKey="Ran J" first="Jinjun" last="Ran">Jinjun Ran</name><affiliation><nlm:aff id="aff0020">School of Public Health, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="Musa, Salihu S" sort="Musa, Salihu S" uniqKey="Musa S" first="Salihu S." last="Musa">Salihu S. Musa</name><affiliation><nlm:aff id="aff0025">Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="Yang, Guangpu" sort="Yang, Guangpu" uniqKey="Yang G" first="Guangpu" last="Yang">Guangpu Yang</name><affiliation><nlm:aff id="aff0030">Department of Orthopaedics and Traumatology, Chinese University of Hong Kong, Hong Kong, China</nlm:aff></affiliation><affiliation><nlm:aff id="aff0035">SH Ho Scoliosis Research Lab, Joint Scoliosis Research Center of Chinese University of Hong Kong and Nanjing University, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="Wang, Weiming" sort="Wang, Weiming" uniqKey="Wang W" first="Weiming" last="Wang">Weiming Wang</name><affiliation><nlm:aff id="aff0040">School of Mathematics and Statistics, Huaiyin Normal University, Huaian, China</nlm:aff></affiliation></author><author><name sortKey="Lou, Yijun" sort="Lou, Yijun" uniqKey="Lou Y" first="Yijun" last="Lou">Yijun Lou</name><affiliation><nlm:aff id="aff0025">Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="Gao, Daozhou" sort="Gao, Daozhou" uniqKey="Gao D" first="Daozhou" last="Gao">Daozhou Gao</name><affiliation><nlm:aff id="aff0045">Department of Mathematics, Shanghai Normal University, Shanghai, China</nlm:aff></affiliation></author><author><name sortKey="Yang, Lin" sort="Yang, Lin" uniqKey="Yang L" first="Lin" last="Yang">Lin Yang</name><affiliation><nlm:aff id="aff0050">School of Nursing, Hong Kong Polytechnic University, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="He, Daihai" sort="He, Daihai" uniqKey="He D" first="Daihai" last="He">Daihai He</name><affiliation><nlm:aff id="aff0025">Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="Wang, Maggie H" sort="Wang, Maggie H" uniqKey="Wang M" first="Maggie H." last="Wang">Maggie H. Wang</name><affiliation><nlm:aff id="aff0005">JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China</nlm:aff></affiliation><affiliation><nlm:aff id="aff0010">Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">32007643</idno><idno type="pmc">7110798</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7110798</idno><idno type="RBID">PMC:7110798</idno><idno type="doi">10.1016/j.ijid.2020.01.050</idno><date when="2020">2020</date><idno type="wicri:Area/Pmc/Corpus">000D57</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000D57</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak</title><author><name sortKey="Zhao, Shi" sort="Zhao, Shi" uniqKey="Zhao S" first="Shi" last="Zhao">Shi Zhao</name><affiliation><nlm:aff id="aff0005">JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China</nlm:aff></affiliation><affiliation><nlm:aff id="aff0010">Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China</nlm:aff></affiliation></author><author><name sortKey="Lin, Qianyin" sort="Lin, Qianyin" uniqKey="Lin Q" first="Qianyin" last="Lin">Qianyin Lin</name><affiliation><nlm:aff id="aff0015">Michigan Institute for Data Science, University of Michigan, Ann Arbor, MI, USA</nlm:aff></affiliation></author><author><name sortKey="Ran, Jinjun" sort="Ran, Jinjun" uniqKey="Ran J" first="Jinjun" last="Ran">Jinjun Ran</name><affiliation><nlm:aff id="aff0020">School of Public Health, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="Musa, Salihu S" sort="Musa, Salihu S" uniqKey="Musa S" first="Salihu S." last="Musa">Salihu S. Musa</name><affiliation><nlm:aff id="aff0025">Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="Yang, Guangpu" sort="Yang, Guangpu" uniqKey="Yang G" first="Guangpu" last="Yang">Guangpu Yang</name><affiliation><nlm:aff id="aff0030">Department of Orthopaedics and Traumatology, Chinese University of Hong Kong, Hong Kong, China</nlm:aff></affiliation><affiliation><nlm:aff id="aff0035">SH Ho Scoliosis Research Lab, Joint Scoliosis Research Center of Chinese University of Hong Kong and Nanjing University, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="Wang, Weiming" sort="Wang, Weiming" uniqKey="Wang W" first="Weiming" last="Wang">Weiming Wang</name><affiliation><nlm:aff id="aff0040">School of Mathematics and Statistics, Huaiyin Normal University, Huaian, China</nlm:aff></affiliation></author><author><name sortKey="Lou, Yijun" sort="Lou, Yijun" uniqKey="Lou Y" first="Yijun" last="Lou">Yijun Lou</name><affiliation><nlm:aff id="aff0025">Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="Gao, Daozhou" sort="Gao, Daozhou" uniqKey="Gao D" first="Daozhou" last="Gao">Daozhou Gao</name><affiliation><nlm:aff id="aff0045">Department of Mathematics, Shanghai Normal University, Shanghai, China</nlm:aff></affiliation></author><author><name sortKey="Yang, Lin" sort="Yang, Lin" uniqKey="Yang L" first="Lin" last="Yang">Lin Yang</name><affiliation><nlm:aff id="aff0050">School of Nursing, Hong Kong Polytechnic University, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="He, Daihai" sort="He, Daihai" uniqKey="He D" first="Daihai" last="He">Daihai He</name><affiliation><nlm:aff id="aff0025">Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China</nlm:aff></affiliation></author><author><name sortKey="Wang, Maggie H" sort="Wang, Maggie H" uniqKey="Wang M" first="Maggie H." last="Wang">Maggie H. Wang</name><affiliation><nlm:aff id="aff0005">JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China</nlm:aff></affiliation><affiliation><nlm:aff id="aff0010">Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China</nlm:aff></affiliation></author></analytic><series><title level="j">International Journal of Infectious Diseases</title><idno type="ISSN">1201-9712</idno><idno type="eISSN">1878-3511</idno><imprint><date when="2020">2020</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><title>Highlights</title><p><list list-type="simple" id="lis0005"><list-item id="lsti0005"><label>•</label><p id="par0005">The novel coronavirus (2019-nCoV) pneumonia has caused 2033 confirmed cases, including 56 deaths in mainland China, by 2020-01-26 17:06.</p></list-item><list-item id="lsti0010"><label>•</label><p id="par0010">We aim to estimate the basic reproduction number of 2019-nCoV in Wuhan, China using the exponential growth model method.</p></list-item><list-item id="lsti0015"><label>•</label><p id="par0015">We estimated that the mean <italic>R</italic><sub>0</sub> ranges from 2.24 to 3.58 with an 8-fold to 2-fold increase in the reporting rate.</p></list-item><list-item id="lsti0020"><label>•</label><p id="par0020">Changes in reporting likely occurred and should be taken into account in the estimation of <italic>R</italic><sub>0</sub>.</p></list-item></list></p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Assiri, A" uniqKey="Assiri A">A. 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Int J Infect Dis</journal-id><journal-id journal-id-type="iso-abbrev">Int. J. Infect. Dis</journal-id><journal-title-group><journal-title>International Journal of Infectious Diseases</journal-title></journal-title-group><issn pub-type="ppub">1201-9712</issn><issn pub-type="epub">1878-3511</issn><publisher><publisher-name>The Author(s). Published by Elsevier Ltd on behalf of International Society for Infectious Diseases.</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">32007643</article-id><article-id pub-id-type="pmc">7110798</article-id><article-id pub-id-type="publisher-id">S1201-9712(20)30053-9</article-id><article-id pub-id-type="doi">10.1016/j.ijid.2020.01.050</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak</article-title></title-group><contrib-group><contrib contrib-type="author" id="aut0005"><name><surname>Zhao</surname><given-names>Shi</given-names></name><email>shi.zhao@link.cuhk.edu.hk</email><xref rid="aff0005" ref-type="aff">a</xref><xref rid="aff0010" ref-type="aff">b</xref><xref rid="cor0005" ref-type="corresp">⁎</xref></contrib><contrib contrib-type="author" id="aut0010"><name><surname>Lin</surname><given-names>Qianyin</given-names></name><email>qianying.lin@connect.polyu.hk</email><xref rid="aff0015" ref-type="aff">c</xref></contrib><contrib contrib-type="author" id="aut0015"><name><surname>Ran</surname><given-names>Jinjun</given-names></name><email>jimran@connect.hku.hk</email><xref rid="aff0020" ref-type="aff">d</xref></contrib><contrib contrib-type="author" id="aut0020"><name><surname>Musa</surname><given-names>Salihu S.</given-names></name><email>salihu-sabiu.musa@connect.polyu.hk</email><xref rid="aff0025" ref-type="aff">e</xref></contrib><contrib contrib-type="author" id="aut0025"><name><surname>Yang</surname><given-names>Guangpu</given-names></name><email>kennethgpy@link.cuhk.edu.hk</email><xref rid="aff0030" ref-type="aff">f</xref><xref rid="aff0035" ref-type="aff">g</xref></contrib><contrib contrib-type="author" id="aut0030"><name><surname>Wang</surname><given-names>Weiming</given-names></name><email>weimingwang2003@163.com</email><xref rid="aff0040" ref-type="aff">h</xref><xref rid="cor0005" ref-type="corresp">⁎</xref></contrib><contrib contrib-type="author" id="aut0035"><name><surname>Lou</surname><given-names>Yijun</given-names></name><email>yijun.lou@polyu.edu.hk</email><xref rid="aff0025" ref-type="aff">e</xref></contrib><contrib contrib-type="author" id="aut0040"><name><surname>Gao</surname><given-names>Daozhou</given-names></name><email>dzgao@shnu.edu.cn</email><xref rid="aff0045" ref-type="aff">i</xref></contrib><contrib contrib-type="author" id="aut0045"><name><surname>Yang</surname><given-names>Lin</given-names></name><email>l.yang@polyu.edu.hk</email><xref rid="aff0050" ref-type="aff">j</xref></contrib><contrib contrib-type="author" id="aut0050"><name><surname>He</surname><given-names>Daihai</given-names></name><email>daihai.he@polyu.edu.hk</email><xref rid="aff0025" ref-type="aff">e</xref><xref rid="cor0005" ref-type="corresp">⁎</xref></contrib><contrib contrib-type="author" id="aut0055"><name><surname>Wang</surname><given-names>Maggie H.</given-names></name><email>maggiew@cuhk.edu.hk</email><xref rid="aff0005" ref-type="aff">a</xref><xref rid="aff0010" ref-type="aff">b</xref></contrib></contrib-group><aff id="aff0005"><label>a</label>JC School of Public Health and Primary Care, Chinese University of Hong Kong, Hong Kong, China</aff><aff id="aff0010"><label>b</label>Shenzhen Research Institute of Chinese University of Hong Kong, Shenzhen, China</aff><aff id="aff0015"><label>c</label>Michigan Institute for Data Science, University of Michigan, Ann Arbor, MI, USA</aff><aff id="aff0020"><label>d</label>School of Public Health, Li Ka Shing Faculty of Medicine, University of Hong Kong, Hong Kong, China</aff><aff id="aff0025"><label>e</label>Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong, China</aff><aff id="aff0030"><label>f</label>Department of Orthopaedics and Traumatology, Chinese University of Hong Kong, Hong Kong, China</aff><aff id="aff0035"><label>g</label>SH Ho Scoliosis Research Lab, Joint Scoliosis Research Center of Chinese University of Hong Kong and Nanjing University, Hong Kong, China</aff><aff id="aff0040"><label>h</label>School of Mathematics and Statistics, Huaiyin Normal University, Huaian, China</aff><aff id="aff0045"><label>i</label>Department of Mathematics, Shanghai Normal University, Shanghai, China</aff><aff id="aff0050"><label>j</label>School of Nursing, Hong Kong Polytechnic University, Hong Kong, China</aff><author-notes><corresp id="cor0005"><label>⁎</label>Corresponding authors. <email>shi.zhao@link.cuhk.edu.hk</email><email>weimingwang2003@163.com</email><email>daihai.he@polyu.edu.hk</email></corresp></author-notes><pub-date pub-type="pmc-release"><day>30</day><month>1</month><year>2020</year></pub-date><pmc-comment> PMC Release delay is 0 months and 0 days and was based on .</pmc-comment>
<pub-date pub-type="ppub"><month>3</month><year>2020</year></pub-date><pub-date pub-type="epub"><day>30</day><month>1</month><year>2020</year></pub-date><volume>92</volume><fpage>214</fpage><lpage>217</lpage><history><date date-type="received"><day>23</day><month>1</month><year>2020</year></date><date date-type="rev-recd"><day>27</day><month>1</month><year>2020</year></date><date date-type="accepted"><day>27</day><month>1</month><year>2020</year></date></history><permissions><copyright-statement>© 2020 The Author(s)</copyright-statement><copyright-year>2020</copyright-year><license><license-p>Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.</license-p></license></permissions><abstract abstract-type="author-highlights" id="abs0005"><title>Highlights</title><p><list list-type="simple" id="lis0005"><list-item id="lsti0005"><label>•</label><p id="par0005">The novel coronavirus (2019-nCoV) pneumonia has caused 2033 confirmed cases, including 56 deaths in mainland China, by 2020-01-26 17:06.</p></list-item><list-item id="lsti0010"><label>•</label><p id="par0010">We aim to estimate the basic reproduction number of 2019-nCoV in Wuhan, China using the exponential growth model method.</p></list-item><list-item id="lsti0015"><label>•</label><p id="par0015">We estimated that the mean <italic>R</italic><sub>0</sub> ranges from 2.24 to 3.58 with an 8-fold to 2-fold increase in the reporting rate.</p></list-item><list-item id="lsti0020"><label>•</label><p id="par0020">Changes in reporting likely occurred and should be taken into account in the estimation of <italic>R</italic><sub>0</sub>.</p></list-item></list></p></abstract><abstract id="abs0010"><sec><title>Backgrounds</title><p>An ongoing outbreak of a novel coronavirus (2019-nCoV) pneumonia hit a major city in China, Wuhan, December 2019 and subsequently reached other provinces/regions of China and other countries. We present estimates of the basic reproduction number, <italic>R</italic><sub>0</sub>, of 2019-nCoV in the early phase of the outbreak.</p></sec><sec><title>Methods</title><p>Accounting for the impact of the variations in disease reporting rate, we modelled the epidemic curve of 2019-nCoV cases time series, in mainland China from January 10 to January 24, 2020, through the exponential growth. With the estimated intrinsic growth rate (<italic>γ</italic>), we estimated <italic>R</italic><sub>0</sub> by using the serial intervals (SI) of two other well-known coronavirus diseases, MERS and SARS, as approximations for the true unknown SI.</p></sec><sec><title>Findings</title><p>The early outbreak data largely follows the exponential growth. We estimated that the mean <italic>R</italic><sub>0</sub> ranges from 2.24 (95%CI: 1.96–2.55) to 3.58 (95%CI: 2.89–4.39) associated with 8-fold to 2-fold increase in the reporting rate. We demonstrated that changes in reporting rate substantially affect estimates of <italic>R</italic><sub>0</sub>.</p></sec><sec><title>Conclusion</title><p>The mean estimate of <italic>R</italic><sub>0</sub> for the 2019-nCoV ranges from 2.24 to 3.58, and is significantly larger than 1. Our findings indicate the potential of 2019-nCoV to cause outbreaks.</p></sec></abstract><kwd-group id="kwd0005"><title>Keywords</title><kwd>Basic reproduction number</kwd><kwd>Novel coronavirus (2019-nCoV)</kwd></kwd-group></article-meta></front><body><sec id="sec0005"><title>Introduction</title><p id="par0025">The atypical pneumonia case, caused by a novel coronavirus (2019-nCoV), was first reported and confirmed in Wuhan, China on December 31, 2019 (<xref rid="bib0090" ref-type="bibr">World Health Organization, 2020a</xref>). As of January 26 (17:00 GMT), 2020, there have been 2033 confirmed cases of 2019-nCoV infections in mainland China, including 56 deaths (<xref rid="bib0060" ref-type="bibr">National Health Commission of the People’s Republic of China, 2020</xref>). The 2019-nCoV cases were also reported in Thailand, Japan, Republic of Korea, Hong Kong, Taiwan and the US, and all of these cases were exported from Wuhan; see the World Health Organization (WHO) news release <ext-link ext-link-type="uri" xlink:href="https://www.who.int/csr/don/en/" id="intr0005">https://www.who.int/csr/don/en/</ext-link> from January 14–21. The outbreak is still ongoing. A recently published preprint by Imai et al. estimated that a total of 1723 (95% CI: 427-4471) cases of 2019-nCoV infections in Wuhan had onset of symptoms by January 12, 2020 (<xref rid="bib0040" ref-type="bibr">Imai et al., 2020</xref>). The likelihood of travel related risks of disease spreading is suggested by <xref rid="bib0015" ref-type="bibr">Bogoch et al. (2020</xref>), which indicates the potentials of regional and global spread (<xref rid="bib0045" ref-type="bibr">Leung et al., 2020</xref>).</p><p id="par0030">To the best of our knowledge, there is no existing peer-reviewed literature quantifying the transmissibility of 2019-nCoV as of January 22, 2020. In this study, we estimated the transmissibility of 2019-nCoV via the basic reproduction number, <italic>R</italic><sub>0</sub>, based on the limited data in the early phase of the outbreak.</p></sec><sec id="sec0010"><title>Methods</title><p id="par0035">We obtained the number of 2019-nCoV cases time series data in mainland China released by Wuhan Municipal Health Commission, China and National Health Commission of China from January 10 to January 24, 2020 from (<xref rid="bib0105" ref-type="bibr">Wuhan Municipal Health Commission, China, 2020</xref>). All cases were laboratory confirmed following the case definition by the National Health Commission of China (<xref rid="bib0060" ref-type="bibr">National Health Commission of the People’s Republic of China, 2020</xref>). Although the date of submission of this study is January 26, we choose to use data up to January 24. Note that the data of the most recent few days contain a number of infections that were infected outside Wuhan due to travel, and thus this part of the infections is excluded from the analysis.</p><p id="par0040">Although there were cases confirmed on or before January 16, the official diagnostic protocol was released by WHO on January 17 (<xref rid="bib0095" ref-type="bibr">World Health Organization, 2020b</xref>). To adjust the impact of this event, we considered a time-varying reporting rate that follows a linear increasing trend, motivated by the previous study (<xref rid="bib0100" ref-type="bibr">Wu et al., 2010</xref>). We assumed that the reporting rate, <italic>r</italic>(<italic>t</italic>), started increasing on January 17, and stopped at the maximal level on January 21. The reporting rate increase corresponds to accounts for the announcement on improving the 2019-nCoV surveillance of the Hubei provincial government (<xref rid="bib0035" ref-type="bibr">Hubei provincial government, 2020</xref>). The length of the reporting increasing part roughly equals the average of the incubation periods of two other well-known coronavirus diseases, i.e., the Middle East Respiratory Syndrome (MERS) and the Severe Acute Respiratory Syndrome (SARS), i.e., 5 days (<xref rid="bib0010" ref-type="bibr">Bauch et al., 2005</xref>, <xref rid="bib0050" ref-type="bibr">Lin et al., 2018</xref>, <xref rid="bib0030" ref-type="bibr">Donnelly et al., 2003</xref>). Denoting the daily reported number of new cases by <italic>c</italic>(<italic>t</italic>) for the <italic>t</italic>-th day, then the adjusted cumulative number of cases, <italic>C</italic>(<italic>t</italic>), is <inline-formula><mml:math id="M1" altimg="si1.svg"><mml:mi>C</mml:mi><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>τ</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow><mml:mi>t</mml:mi></mml:msubsup><mml:mi>c</mml:mi><mml:mo>(</mml:mo><mml:mi>τ</mml:mi><mml:mo>)</mml:mo><mml:mo>/</mml:mo><mml:mi>r</mml:mi><mml:mo>(</mml:mo><mml:mi>τ</mml:mi><mml:mo>)</mml:mo></mml:math></inline-formula>. Instead of finding the exact value of <italic>r</italic>(<italic>t</italic>), we calculated the fold change in <italic>r</italic>(<italic>t</italic>) that is defined by the ratio of <italic>r</italic> on January 10 over that on January 24 minus 1. We illustrated six scenarios with 0- (no change), 0.5-, 1-, 2-, 4- and 8-fold increase in reporting rate, see <xref rid="fig0005" ref-type="fig">Figure 1</xref>(a), (c), (e), (g), (i) and (k).<fig id="fig0005"><label>Figure 1</label><caption><p>The scenarios of the change in the reporting rate (top panels) and the exponential growth fitting (bottom panels). The top panels, i.e., (a), (c), (e), (g), (i) and (k), show the assumed change in the reporting rate. The bottom panels, i.e., (b), (d), (f), (h), (j) and (l), show the reported (or observed, green circles), adjusted (blue dots) and fitted (blue curve) number of 2019-nCoV infections, and the blue dashed lines are the 95%CI. The vertical grey line represents the date of January 16, 2020, after which the official diagnostic protocol was released by the WHO (World Health Organization, 2020). Panels (a) and (b) show the scenarios that the reporting rate was unchanged. Panels (c) and (d) show the scenarios that the reporting rate increased by 0.5-fold. Panels (e) and (f) show the scenarios that the reporting rate increased by 1-fold. Panels (g) and (h) show the scenarios that the reporting rate increased by 2-fold. Panels (i) and (j) show the scenarios that the reporting rate increased by 4-fold. Panels (k) and (l) show the scenarios that the reporting rate increased by 8-fold.</p></caption><alt-text id="at0005">Figure 1</alt-text><graphic xlink:href="gr1_lrg"></graphic></fig></p><p id="par0045">Following previous studies (<xref rid="bib0110" ref-type="bibr">Zhao et al., 2019</xref>, <xref rid="bib0025" ref-type="bibr">de Silva et al., 2009</xref>), we modelled the epidemic curve obeying the exponential growth. The nonlinear least square (NLS) framework is adopted for data fitting and parameter estimation. The intrinsic growth rate (<italic>γ</italic>) of the exponential growth was estimated, and the basic reproduction number could be obtained by <italic>R</italic><sub>0</sub> = 1/<italic>M</italic>(−<italic>γ</italic>) with 100% susceptibility for 2019-nCoV at this early stage. The function <italic>M</italic>(∙) is the Laplace transform, i.e., the moment generating function, of the probability distribution for the serial interval (SI) of the disease (<xref rid="bib0110" ref-type="bibr">Zhao et al., 2019</xref>, <xref rid="bib0080" ref-type="bibr">Wallinga and Lipsitch, 2007</xref>), denoted by <italic>h</italic>(<italic>k</italic>) and <italic>k</italic> is the mean SI. Since the transmission chain of 2019-nCoV remains unclear, we adopted the SI information from SARS and MERS, which share a similar pathogen as 2019-nCoV. We modelled <italic>h</italic>(<italic>k</italic>) as Gamma distributions with a mean of 7.6 days and standard deviation (SD) of 3.4 days for MERS (<xref rid="bib0005" ref-type="bibr">Assiri et al., 2013</xref>), and mean of 8.4 days and SD of 3.8 days for SARS (<xref rid="bib0055" ref-type="bibr">Lipsitch et al., 2003</xref>) as well as their average, see the row heads in <xref rid="tbl0005" ref-type="table">Table 1</xref>for each scenario.<table-wrap position="float" id="tbl0005"><label>Table 1</label><caption><p>The summary table of the estimated basic reproduction number, <italic>R</italic><sub>0</sub>, under different scenarios. The estimated <italic>R</italic><sub>0</sub> is shown as in the ‘median (95%CI)’ format. The ‘reporting rate increased’ indicates the number of fold increase in the reporting rate from January 17, when WHO released the official diagnostic protocol (<xref rid="bib0095" ref-type="bibr">World Health Organization, 2020b</xref>), to January 20, 2020.</p></caption><alt-text id="at0010">Table 1</alt-text><table frame="hsides" rules="groups"><thead><tr><th align="left" valign="middle" rowspan="2">Reporting rate increased</th><th colspan="3" align="left">Estimated <italic>R</italic><sub>0</sub><hr></hr></th></tr><tr><th align="left">Same as MERS SI 7.6 ± 3.4</th><th align="left">SI in average 8.0 ± 3.6</th><th align="left">Same as SARS SI 8.4 ± 3.8</th></tr></thead><tbody><tr><td align="left">(unchanged)</td><td align="left">5.31 (3.99–6.96)</td><td align="left">5.71 (4.24–7.54)</td><td align="left">6.11 (4.51–8.16)</td></tr><tr><td align="left">0.5-fold</td><td align="left">4.52 (3.49–5.76)</td><td align="left">4.82 (3.69–6.20)</td><td align="left">5.14 (3.90–6.67)</td></tr><tr><td align="left">1-fold</td><td align="left">4.01 (3.17–5.02)</td><td align="left">4.26 (3.34–5.38)</td><td align="left">4.53 (3.51–5.76)</td></tr><tr><td align="left">2-fold</td><td align="left">3.38 (2.75–4.12)</td><td align="left">3.58 (2.89–4.39)</td><td align="left">3.77 (3.02–4.67)</td></tr><tr><td align="left">4-fold</td><td align="left">2.73 (2.31–3.22)</td><td align="left">2.86 (2.40–3.39)</td><td align="left">3.00 (2.50–3.58)</td></tr><tr><td align="left">8-fold</td><td align="left">2.16 (1.90–2.45)</td><td align="left">2.24 (1.96–2.55)</td><td align="left">2.32 (2.02–2.66)</td></tr></tbody></table><table-wrap-foot><fn><p><italic>Note</italic>: ‘SI’ is serial interval. ‘MERS’ is Middle East Respiratory Syndrome, and ‘SARS’ is the Severe Acute Respiratory Syndrome.</p></fn></table-wrap-foot></table-wrap></p></sec><sec id="sec0015"><title>Results and discussion</title><p id="par0050">The exponential growth fitting results are shown in <xref rid="fig0005" ref-type="fig">Figure 1</xref>(b), (d), (f), (h), (j) and (l). The coefficient of determination, R-squared, ranges from 0.91 to 0.92 for all reporting rate changing scenarios, which implies that the early outbreak data were largely following the exponential growth. In <xref rid="tbl0005" ref-type="table">Table 1</xref>, we estimated that the <italic>R</italic><sub>0</sub> ranges from 2.24 (95%CI: 1.96-2.55) to 5.71 (95%CI: 4.24-7.54) associated with an 8-fold to 0-fold increase in the reporting rate. All <italic>R</italic><sub>0</sub> estimates are significantly larger than 1, which indicates the potential of 2019-nCoV to cause outbreaks. Since the official diagnostic protocol was released by WHO on January 17 (<xref rid="bib0095" ref-type="bibr">World Health Organization, 2020b</xref>), an increase in the diagnosis and reporting of 2019-nCoV infections probably occurred. Thereafter, the daily number of newly reported cases started increasing around January 17, see <xref rid="fig0005" ref-type="fig">Figure 1</xref>, which implies that more infections were likely being diagnosed and recorded. We suggested that changes in reporting might exist, and thus it should be considered in the estimation, i.e., 8-, 4- and 2-fold changes are more likely than no change in the reporting efforts. Although six scenarios about the reporting rate were explored in this study, the real situation is difficult to determine given limited data and (almost) equivalent model fitting performance in terms of R-squared. However, with increasing reporting rate, we found the mean <italic>R</italic><sub>0</sub> is likely to be between 2 and 3.</p><p id="par0055">Our analysis and estimation of <italic>R</italic><sub>0</sub> rely on the accuracy of the SI of 2019-nCoV, which remains unknown as of January 25. In this work, we employed the SIs of SARS and MERS as approximations to that of 2019-nCoV. The determination of SI requires knowledge of the chain of disease transmission that needs a sufficient number of patient samples and periods of time for follow-up (<xref rid="bib0020" ref-type="bibr">Cowling et al., 2009</xref>), and thus this is unlikely to be achieved shortly. However, using SIs of SARS and MERS as approximation could provide an insight to the transmission potential of 2019-nCoV at the early stage of the outbreak. We reported that the mean <italic>R</italic><sub>0</sub> of 2019-nCoV is likely to be from 2.24 (8-fold) to 3.58 (2-fold), and it is largely in the range of those of SARS, i.e., 2-5 (<xref rid="bib0010" ref-type="bibr">Bauch et al., 2005</xref>, <xref rid="bib0055" ref-type="bibr">Lipsitch et al., 2003</xref>, <xref rid="bib0085" ref-type="bibr">Wallinga and Teunis, 2004</xref>), and MERS, i.e., 2.7-3.9 (<xref rid="bib0050" ref-type="bibr">Lin et al., 2018</xref>).</p><p id="par0060">We note that WHO reported the basic reproduction number for the human-to-human (direct) transmission ranged from 1.4 to 2.5 (<xref rid="bib0095" ref-type="bibr">World Health Organization, 2020b</xref>), which is marginally lower than ours. However, many of the existing online preprints estimate the mean <italic>R</italic><sub>0</sub> ranging from 2 to 5 (<xref rid="bib0040" ref-type="bibr">Imai et al., 2020</xref>, <xref rid="bib0070" ref-type="bibr">Riou and Althaus, 2020</xref>, <xref rid="bib0065" ref-type="bibr">Read et al., 2020</xref>, <xref rid="bib0075" ref-type="bibr">Shen et al., 2020</xref>), which is largely consistent with our results.</p></sec><sec id="sec0020"><title>Conclusion</title><p id="par0065">We estimated the mean <italic>R</italic><sub>0</sub> of 2019-nCoV ranging from 2.24 (95%CI: 1.96-2.55) to 3.58 (95%CI: 2.89-4.39) if the reporting effort has been increased by a factor of between 8- and 2-fold, respectively, after the diagnostic protocol released on January 17, 2020 and many medical supplies reached Wuhan.</p></sec><sec id="sec0025"><title>Ethics approval and consent to participate</title><p id="par0070">The ethical approval or individual consent was not applicable.</p></sec><sec sec-type="data-availability" id="sec0030"><title>Availability of data and materials</title><p id="par0075">All data and materials used in this work were publicly available.</p></sec><sec id="sec0035"><title>Consent for publication</title><p id="par0080">Not applicable.</p></sec><sec id="sec0040"><title>Funding</title><p id="par0085">DH was supported by <funding-source id="gs0005">General Research Fund</funding-source> (Grant Number 15205119) of the Research Grants Council (RGC) of Hong Kong, China. WW was supported by <funding-source id="gs0010">National Natural Science Foundation of China</funding-source> (Grant Number 61672013) and <funding-source id="gs0015">Huaian Key Laboratory for Infectious Diseases Control and Prevention</funding-source> (Grant Number HAP201704), Huaian, Jiangsu, China.</p></sec><sec id="sec0045"><title>Disclaimer</title><p id="par0090">The funding agencies had no role in the design and conduct of the study; collection, management, analysis, and interpretation of the data; preparation, review, or approval of the manuscript; or decision to submit the manuscript for publication.</p></sec><sec id="sec0050"><title>Conflict of interests</title><p id="par0095">The authors declare no competing interests.</p></sec><sec id="sec0055"><title>Authors contributions</title><p id="par0100">All authors conceived the study, carried out the analysis, discussed the results, drafted the first manuscript, critically read and revised the manuscript, and gave final approval for 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