Simulating and forecasting the cumulative confirmed cases of SARS-CoV-2 in China by Boltzmann function-based regression analyses
Identifieur interne : 000A98 ( Pmc/Corpus ); précédent : 000A97; suivant : 000A99Simulating and forecasting the cumulative confirmed cases of SARS-CoV-2 in China by Boltzmann function-based regression analyses
Auteurs : Xinmiao Fu ; Qi Ying ; Tieyong Zeng ; Tao Long ; Yan WangSource :
- The Journal of Infection [ 0163-4453 ] ; 2020.
Abstract
Cumulative confirmed cases in China were well fitted with Boltzmann function. Potential total numbers of confirmed cases in different regions were estimated. Key dates indicating minimal daily number of new confirmed cases were estimated. Cumulative confirmed cases of 2003 SARS-CoV were well fitted to Boltzmann function. The Boltzmann function was, for the first time, applied to epidemic analysis.
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DOI: 10.1016/j.jinf.2020.02.019
PubMed: 32112887
PubMed Central: 7127674
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Simulating and forecasting the cumulative confirmed cases of SARS-CoV-2 in China by Boltzmann function-based regression analyses</title><author><name sortKey="Fu, Xinmiao" sort="Fu, Xinmiao" uniqKey="Fu X" first="Xinmiao" last="Fu">Xinmiao Fu</name><affiliation><nlm:aff id="aff0001">Provincial University Key Laboratory of Cellular Stress Response and Metabolic Regulation, College of Life Sciences, Fujian Normal University (Qishan campus), Room 214, Ligong Building, Fuzhou, Fujian 350117, China</nlm:aff></affiliation></author><author><name sortKey="Ying, Qi" sort="Ying, Qi" uniqKey="Ying Q" first="Qi" last="Ying">Qi Ying</name><affiliation><nlm:aff id="aff0002">Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX 77843, USA</nlm:aff></affiliation></author><author><name sortKey="Zeng, Tieyong" sort="Zeng, Tieyong" uniqKey="Zeng T" first="Tieyong" last="Zeng">Tieyong Zeng</name><affiliation><nlm:aff id="aff0003">Department of mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong 99999, China</nlm:aff></affiliation></author><author><name sortKey="Long, Tao" sort="Long, Tao" uniqKey="Long T" first="Tao" last="Long">Tao Long</name><affiliation><nlm:aff id="aff0004">Nanjing Institute of Environmental Sciences, Ministry of Ecology and Environment, China</nlm:aff></affiliation></author><author><name sortKey="Wang, Yan" sort="Wang, Yan" uniqKey="Wang Y" first="Yan" last="Wang">Yan Wang</name><affiliation><nlm:aff id="aff0001">Provincial University Key Laboratory of Cellular Stress Response and Metabolic Regulation, College of Life Sciences, Fujian Normal University (Qishan campus), Room 214, Ligong Building, Fuzhou, Fujian 350117, China</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">32112887</idno><idno type="pmc">7127674</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7127674</idno><idno type="RBID">PMC:7127674</idno><idno type="doi">10.1016/j.jinf.2020.02.019</idno><date when="2020">2020</date><idno type="wicri:Area/Pmc/Corpus">000A98</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000A98</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Simulating and forecasting the cumulative confirmed cases of SARS-CoV-2 in China by Boltzmann function-based regression analyses</title><author><name sortKey="Fu, Xinmiao" sort="Fu, Xinmiao" uniqKey="Fu X" first="Xinmiao" last="Fu">Xinmiao Fu</name><affiliation><nlm:aff id="aff0001">Provincial University Key Laboratory of Cellular Stress Response and Metabolic Regulation, College of Life Sciences, Fujian Normal University (Qishan campus), Room 214, Ligong Building, Fuzhou, Fujian 350117, China</nlm:aff></affiliation></author><author><name sortKey="Ying, Qi" sort="Ying, Qi" uniqKey="Ying Q" first="Qi" last="Ying">Qi Ying</name><affiliation><nlm:aff id="aff0002">Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX 77843, USA</nlm:aff></affiliation></author><author><name sortKey="Zeng, Tieyong" sort="Zeng, Tieyong" uniqKey="Zeng T" first="Tieyong" last="Zeng">Tieyong Zeng</name><affiliation><nlm:aff id="aff0003">Department of mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong 99999, China</nlm:aff></affiliation></author><author><name sortKey="Long, Tao" sort="Long, Tao" uniqKey="Long T" first="Tao" last="Long">Tao Long</name><affiliation><nlm:aff id="aff0004">Nanjing Institute of Environmental Sciences, Ministry of Ecology and Environment, China</nlm:aff></affiliation></author><author><name sortKey="Wang, Yan" sort="Wang, Yan" uniqKey="Wang Y" first="Yan" last="Wang">Yan Wang</name><affiliation><nlm:aff id="aff0001">Provincial University Key Laboratory of Cellular Stress Response and Metabolic Regulation, College of Life Sciences, Fujian Normal University (Qishan campus), Room 214, Ligong Building, Fuzhou, Fujian 350117, China</nlm:aff></affiliation></author></analytic><series><title level="j">The Journal of Infection</title><idno type="ISSN">0163-4453</idno><idno type="eISSN">1532-2742</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="celist0001"><list-item id="celistitem0001"><label>•</label><p id="para0001">Cumulative confirmed cases in China were well fitted with Boltzmann function.</p></list-item><list-item id="celistitem0002"><label>•</label><p id="para0002">Potential total numbers of confirmed cases in different regions were estimated.</p></list-item><list-item id="celistitem0003"><label>•</label><p id="para0003">Key dates indicating minimal daily number of new confirmed cases were estimated.</p></list-item><list-item id="celistitem0004"><label>•</label><p id="para0004">Cumulative confirmed cases of 2003 SARS-CoV were well fitted to Boltzmann function.</p></list-item><list-item id="celistitem0005"><label>•</label><p id="para0005">The Boltzmann function was, for the first time, applied to epidemic analysis.</p></list-item></list></p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Tang, J W" uniqKey="Tang J">J.W. Tang</name></author><author><name sortKey="Tambyah, P A" uniqKey="Tambyah P">P.A. Tambyah</name></author><author><name sortKey="Hui, D S C" uniqKey="Hui D">D.S.C. Hui</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Wang, C" uniqKey="Wang C">C. Wang</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Wu, F" uniqKey="Wu F">F. Wu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Zhou, P" uniqKey="Zhou P">P. Zhou</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lu, R" uniqKey="Lu R">R. Lu</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Wu, J T" uniqKey="Wu J">J.T. Wu</name></author><author><name sortKey="Leung, K" uniqKey="Leung K">K. Leung</name></author><author><name sortKey="Leung, G M" uniqKey="Leung G">G.M. Leung</name></author></analytic></biblStruct><biblStruct></biblStruct><biblStruct><analytic><author><name sortKey="Huang, N E" uniqKey="Huang N">N.E. Huang</name></author><author><name sortKey="Qiao, F" uniqKey="Qiao F">F. Qiao</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="letter"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">J Infect</journal-id><journal-id journal-id-type="iso-abbrev">J. Infect</journal-id><journal-title-group><journal-title>The Journal of Infection</journal-title></journal-title-group><issn pub-type="ppub">0163-4453</issn><issn pub-type="epub">1532-2742</issn><publisher><publisher-name>The British Infection Association. Published by Elsevier Ltd.</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">32112887</article-id><article-id pub-id-type="pmc">7127674</article-id><article-id pub-id-type="publisher-id">S0163-4453(20)30098-0</article-id><article-id pub-id-type="doi">10.1016/j.jinf.2020.02.019</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Simulating and forecasting the cumulative confirmed cases of SARS-CoV-2 in China by Boltzmann function-based regression analyses</article-title></title-group><contrib-group><contrib contrib-type="author" id="au0001"><name><surname>Fu</surname><given-names>Xinmiao</given-names></name><email>xmfu@fjnu.edu.cn</email><xref rid="aff0001" ref-type="aff">a</xref><xref rid="cor0001" ref-type="corresp">⁎</xref></contrib><contrib contrib-type="author" id="au0002"><name><surname>Ying</surname><given-names>Qi</given-names></name><xref rid="aff0002" ref-type="aff">b</xref></contrib><contrib contrib-type="author" id="au0003"><name><surname>Zeng</surname><given-names>Tieyong</given-names></name><xref rid="aff0003" ref-type="aff">c</xref></contrib><contrib contrib-type="author" id="au0004"><name><surname>Long</surname><given-names>Tao</given-names></name><xref rid="aff0004" ref-type="aff">d</xref></contrib><contrib contrib-type="author" id="au0005"><name><surname>Wang</surname><given-names>Yan</given-names></name><xref rid="aff0001" ref-type="aff">a</xref></contrib></contrib-group><aff id="aff0001"><label>a</label>Provincial University Key Laboratory of Cellular Stress Response and Metabolic Regulation, College of Life Sciences, Fujian Normal University (Qishan campus), Room 214, Ligong Building, Fuzhou, Fujian 350117, China</aff><aff id="aff0002"><label>b</label>Department of Civil and Environmental Engineering, Texas A&M University, College Station, TX 77843, USA</aff><aff id="aff0003"><label>c</label>Department of mathematics, The Chinese University of Hong Kong, Shatin, NT, Hong Kong 99999, China</aff><aff id="aff0004"><label>d</label>Nanjing Institute of Environmental Sciences, Ministry of Ecology and Environment, China</aff><author-notes><corresp id="cor0001"><label>⁎</label>Corresponding author. <email>xmfu@fjnu.edu.cn</email></corresp></author-notes><pub-date pub-type="pmc-release"><day>26</day><month>2</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>5</month><year>2020</year></pub-date><pub-date pub-type="epub"><day>26</day><month>2</month><year>2020</year></pub-date><volume>80</volume><issue>5</issue><fpage>578</fpage><lpage>606</lpage><history><date date-type="accepted"><day>21</day><month>2</month><year>2020</year></date></history><permissions><copyright-statement>© 2020 The British Infection Association. Published by Elsevier Ltd. All rights reserved.</copyright-statement><copyright-year>2020</copyright-year><copyright-holder></copyright-holder><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="abs0001"><title>Highlights</title><p><list list-type="simple" id="celist0001"><list-item id="celistitem0001"><label>•</label><p id="para0001">Cumulative confirmed cases in China were well fitted with Boltzmann function.</p></list-item><list-item id="celistitem0002"><label>•</label><p id="para0002">Potential total numbers of confirmed cases in different regions were estimated.</p></list-item><list-item id="celistitem0003"><label>•</label><p id="para0003">Key dates indicating minimal daily number of new confirmed cases were estimated.</p></list-item><list-item id="celistitem0004"><label>•</label><p id="para0004">Cumulative confirmed cases of 2003 SARS-CoV were well fitted to Boltzmann function.</p></list-item><list-item id="celistitem0005"><label>•</label><p id="para0005">The Boltzmann function was, for the first time, applied to epidemic analysis.</p></list-item></list></p></abstract><kwd-group id="keys0001"><title>Keywords</title><kwd>SARS-CoV-2</kwd><kwd>2019-nCoV</kwd><kwd>Boltzmann function</kwd><kwd>Coronavirus</kwd><kwd>SARS</kwd><kwd>Epidemic</kwd><kwd>Modeling studies</kwd></kwd-group></article-meta></front><body><p content-type="salutation"><italic>Dear editor</italic>,</p><p id="para0007">As reported in this Journal<xref rid="bib0001" ref-type="bibr"><sup>1</sup></xref> and elsewhere,<xref rid="bib0002" ref-type="bibr"><sup>2</sup></xref> an outbreak of atypical pneumonia caused by the zoonotic 2019 novel coronavirus (SARS-CoV-2) is on-going in China and has spread to the world. As of Feb 16, 2020 (24:00, GMT+8), there have been 70,548 confirmed patients and more than 1700 deaths from SARS-CoV-2 infection in China, and 58,182 confirmed patients and 1696 deaths in the most affected province, Hubei Province. Much research progress has been made in dissecting the evolution and origin of SARS-CoV-2 and characterizing its clinical features.<xref rid="bib0003" ref-type="bibr">3</xref>, <xref rid="bib0004" ref-type="bibr">4</xref>, <xref rid="bib0005" ref-type="bibr">5</xref>, <xref rid="bib0006" ref-type="bibr">6</xref>, <xref rid="bib0007" ref-type="bibr">7</xref></p><p id="para0008">While the outbreak is on-going, people raise grave concerns about the future trajectory of the outbreak, especially given that the working and schooling time has been already dramatically postponed after the Chinese Lunar New Year holiday was over (scheduled on Jan 31). In particular, a precise estimation of the potential total number of infected cases and/or confirmed cases is highly demanding. Earlier studies based on susceptible-exposed-infectious-recovered metapopulation and susceptible-infected-recovered-dead models revealed the number of potentially infected cases and the basic reproductive number of SARS-CoV-2.<xref rid="bib0003" ref-type="bibr"><sup>3</sup></xref><sup>,</sup><xref rid="bib0008" ref-type="bibr"><sup>8</sup></xref><sup>,</sup><xref rid="bib0009" ref-type="bibr"><sup>9</sup></xref> These traditional epidemiological models apparently require much detailed data for analysis.<xref rid="bib0003" ref-type="bibr"><sup>3</sup></xref><sup>,</sup><xref rid="bib0008" ref-type="bibr"><sup>8</sup></xref></p><p id="para0009">Here we explored a simple data-driven, Boltzmann function-based approach for estimation only based on the daily cumulative number of confirmed cases of SARS-CoV-2 (Note: the rational for Boltzmann function-based regression analysis is presented in supporting information (SI) file). We decided to collect data (initially from Jan 21 to Feb 10, 2020) in several typical regions of China, including the center of the outbreak (i.e. Wuhan City and Hubei Province), other four most affected provinces (i.e., Guangdong, Zhejiang, Henan, Hunan) and top-4 major cities in China (i.e., Beijing, Shanghai, Guangzhou, Shenzhen). During data analysis on Feb 13, 2020, the number of new confirmed cases on Feb 12 in Hubei Province and Wuhan City suddenly increased by 14,840 and 13,436, respectively, of which 13,332 and 12,364 are those confirmed by clinical features (note: all the number of confirmed cases released by Feb 12 were counted according to the result of viral nucleic acid detection rather than by referring to clinical features). We thus arbitrarily distributed these suddenly added cases to the reported cumulative number of confirmed cases from Jan 21 to Feb 14 for Hubei Province by a fixed factor (refer to <bold>Table S1</bold>), assuming that they were linearly accumulative in those days. It is the same forth with the data for Wuhan City.</p><p id="para0010">Regression analyses indicate that all sets of data were well fitted with the Boltzmann function (all <italic>R<sup>2</sup></italic> values being close to 0.999; <xref rid="fig0001" ref-type="fig">Figs. 1</xref>A, B, <bold>S1</bold>, and <xref rid="tbl0001" ref-type="table">Table 1</xref>). The potential total number of confirmed cases for mainland China, Hubei Province, Wuhan City, and other provinces were estimated as 72,800±600, 59,300±600, 42,100±700 and 12,800±100; respectively; those for provinces Guangdong, Zhejiang, Henan and Hunan were 1300±10, 1170±10, 1260±10, 1050±10, 1020±10 and 940±10, respectively (<xref rid="tbl0001" ref-type="table">Table 1</xref>); those for Beijing, Shanghai, Guangzhou and Shenzhen were 394±4, 328±3, 337±3 and 397±4, respectively. In addition, we estimated the key date, on which the number of daily new confirmed cases is lower than 0.1% of the potential total number as defined by us subjectively (refer to <xref rid="tbl0001" ref-type="table">Table 1</xref>).<fig id="fig0001"><label>Fig. 1</label><caption><p>Fitting the cumulative number of confirmed cases from different geographic regions of China to the Boltzmann function.</p><p>(<bold>A</bold>) Plots of the cumulative number of confirmed cases of SARS-CoV-2 as of Feb 14, 2020, in mainland China (■), in Hubei Province (□), in Wuhan City (▲) and in other provinces (△), with the simulation results being plotted as color lines. Note: the reported cumulative number of confirmed cases of Hubei Province and Wuhan City were re-adjusted for data fitting due to the suddenly added cases by clinical features (for detail, refer to <bold>Table S1</bold>). (<bold>B</bold>) Plots of the cumulative number of confirmed cases of SARS-CoV-2 as of Feb 14, 2020, in the most affected provinces (Guangdong, ■; Zhejiang, □; Henan, ▲; Hunan, △), with the simulation results being plotted as color lines. (<bold>C, D</bold>) Data of mainland China (panel C) and Hubei Province (panel D) were fitted to the Boltzmann function assuming that the relative uncertainty of the data follows a single-sided normal distribution with a mean of 1.0 and a standard deviation of 10%. Original data are shown as circles; simulated results are presented as colored lines as indicated. Inserts show key statistics. The key date is defined as the date when the number of daily new confirmed cases is less than 0.1% of the potential total number. The low and high key dates were determined by the simulated curve of confidence interval (CI) at 2.5% and 97.5%, respectively. (<bold>E, F</bold>) The cumulative number of confirmed cases of 2003 SARS in China (panel E) and worldwide (panel F) are shown as black squares, and the simulation results are plotted as red short lines and parameters of each established function are shown in inserts. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)</p></caption><alt-text id="alt0001">Fig. 1</alt-text><graphic xlink:href="gr1_lrg"></graphic></fig><table-wrap position="float" id="tbl0001"><label>Table 1</label><caption><p>Regression analysis results of confirmed cases of SARS-CoV-2 in China.</p></caption><alt-text id="alt0002">Table 1</alt-text><table frame="hsides" rules="groups"><thead><tr><th rowspan="2" align="left" valign="top">Regions</th><th colspan="3" align="left" valign="top">without uncertainty<hr></hr></th><th colspan="2" align="left" valign="top">with uncertainty<xref rid="tb1fn1" ref-type="table-fn">a</xref><hr></hr></th></tr><tr><th valign="top">potential total number</th><th valign="top">key date<xref rid="tb1fn2" ref-type="table-fn">b</xref></th><th valign="top"><italic>R<sup>2</sup></italic></th><th valign="top">potential total number (mean, 95% CI)</th><th valign="top">key date (95% CI)<xref rid="tb1fn2" ref-type="table-fn">b</xref></th></tr></thead><tbody><tr><td valign="top">China</td><td valign="top">72,800±600</td><td valign="top">2/28</td><td valign="top">0.999</td><td valign="top">79,589 (71,576, 93,855)</td><td valign="top">(2/28, 3/10)</td></tr><tr><td valign="top">Hubei Province</td><td valign="top">59,300±600</td><td valign="top">2/27</td><td valign="top">0.999</td><td valign="top">64,817 (58,223, 77,895)</td><td valign="top">(2/27, 3/10)</td></tr><tr><td valign="top">Wuhan City</td><td valign="top">42,100±700</td><td valign="top">2/27</td><td valign="top">0.999</td><td valign="top">46,562 (40,812, 57,678)</td><td valign="top">(2/28, 3/10)</td></tr><tr><td valign="top">Other provinces</td><td valign="top">12,800±100</td><td valign="top">2/27</td><td valign="top">0.999</td><td valign="top">13,956 (12,748, 16,092)</td><td valign="top">(2/27, 3/13)</td></tr><tr><td valign="top">Guangdong Province</td><td valign="top">1300±10</td><td valign="top">2/22</td><td valign="top">0.999</td><td valign="top">1415 (1324, 1550)</td><td valign="top">(2/22, 3/01)</td></tr><tr><td valign="top">Zhejiang Province</td><td valign="top">1170±10</td><td valign="top">2/20</td><td valign="top">0.997</td><td valign="top">1269 (1204, 1364)</td><td valign="top">(2/21, 2/27)</td></tr><tr><td valign="top">Henan Province</td><td valign="top">1260±10</td><td valign="top">2/24</td><td valign="top">0.999</td><td valign="top">1372 (1271, 1559)</td><td valign="top">(2/26, 3/09)</td></tr><tr><td valign="top">Hunan Province</td><td valign="top">1050±10</td><td valign="top">2/26</td><td valign="top">0.999</td><td valign="top">1140 (1050, 1279)</td><td valign="top">(2/28, 3/11)</td></tr><tr><td valign="top">Beijing City</td><td valign="top">394±4</td><td valign="top">2/25</td><td valign="top">0.999</td><td valign="top">429 (395, 486)</td><td valign="top">(2/25, 3/11)</td></tr><tr><td valign="top">Shanghai City</td><td valign="top">328±3</td><td valign="top">2/22</td><td valign="top">0.999</td><td valign="top">356 (334, 388)</td><td valign="top">(2/22, 3/01)</td></tr><tr><td valign="top">Guangzhou City</td><td valign="top">337±3</td><td valign="top">2/20</td><td valign="top">0.998</td><td valign="top">365 (346, 393)</td><td valign="top">(2/20, 2/28)</td></tr><tr><td valign="top">Shenzhen City</td><td valign="top">397±4</td><td valign="top">2/18</td><td valign="top">0.998</td><td valign="top">430 (407, 461)</td><td valign="top">(2/17, 2/25)</td></tr></tbody></table><table-wrap-foot><fn id="tb1fn1"><label>a</label><p id="notep0001">The reported cumulative number of confirmed cases may have uncertainty. Assuming the relative uncertainty follows a single-sided normal distribution with a mean of 1.0 and a standard deviation of 10%, the potential total number and key dates were estimated at 95% CI. For detail, refer to the Methods section and <xref rid="fig0001" ref-type="fig">Figs. 1</xref>C, D, <bold>S2</bold> and <bold>S3.</bold></p></fn></table-wrap-foot><table-wrap-foot><fn id="tb1fn2"><label>b</label><p id="notep0002">Key date is determined when the number of daily new confirmed cases is less than 0.1% of the potential total number.</p></fn></table-wrap-foot></table-wrap></p><p id="para0011">The above analyses were performed assuming that the released data on the confirmed cases are precise. However, there is a tendency to miss-report some positive cases such that the reported numbers represent a lower limit. One typical example indicating this uncertainty is the sudden increase of more than 14 000 new confirmed cases in Hubei Province on Feb 12 after clinical features were officially accepted as a standard for infection confirmation. Another uncertainty might result from insufficient kits for viral nucleic acid detection at the early stage of the outbreak. We thus examined the effects of such uncertainty using a Monte Carlo method (for detail, refer to the Methods section in SI file). For simplicity, we assumed that the relative uncertainty of the reported data follows a single-sided normal distribution with a mean of 1.0 and a standard deviation of 10%.</p><p id="para0012">Under the above conditions, the potential total numbers of confirmed cases of SARS-CoV-2 for different regions were estimated (<xref rid="fig0001" ref-type="fig">Figs. 1</xref>C, D, <bold>S2</bold> and <bold>S3</bold>) and summarized in <xref rid="tbl0001" ref-type="table">Table 1</xref>. The potential total numbers for China, Hubei Province, Wuhan City and other provinces were 79,589 (95% CI 71,576, 93,855), 64,817 (58,223, 77,895), 46,562 (40,812, 57,678) and 13,956 (12,748, 16,092), respectively, indicating that overall the outbreak may not be so bad as previously estimated.<xref rid="bib0009" ref-type="bibr"><sup>9</sup></xref> Such uncertainty analysis also allowed us to estimate the key dates at 95% CI. As summarized in <xref rid="tbl0001" ref-type="table">Table 1</xref>, the key dates for mainland China, Hubei Province, Wuhan City, and other provinces would fall in (2/28, 3/10), (2/27, 3/10), (2/28, 3/10) and (2/27, 3/13), respectively.</p><p id="para0013">Finally, the ongoing SARS-CoV-2 outbreak has undoubtedly caused us the memories of the SARS-CoV outbreak in 2003. We thus collected the data from the WHO officiate website for analysis, and found that the cumulative numbers of confirmed cases of 2003 SARS-CoV both in China and worldwide were fitted well with the Boltzmann function, with <italic>R<sup>2</sup></italic> being 0.999 and 0.998, respectively (<xref rid="fig0001" ref-type="fig">Figs. 1</xref>E and F).</p><p id="para0014">In summary, we found that all data sets, including both the on-going outbreak of SARS-CoV-2 in China and the 2003 SARS-CoV epidemic in China and worldwide, were well fitted to the Boltzmann function (<xref rid="fig0001" ref-type="fig">Fig. 1</xref> and <bold>S1</bold>). These results strongly suggest that the Boltzmann function is suitable for analyzing the epidemics of coronaviruses like SARS-CoV and SARS-CoV-2. One advantage of this model is that it only needs the cumulative number of confirmed cases, somehow as simple as the recently proposed model.<xref rid="bib0010" ref-type="bibr"><sup>10</sup></xref> In addition, the estimated potential total numbers of confirmed cases and key dates may provide valuable guidance for Chinese central and local governments to deal with this emerging threat at current critical stage.</p><sec sec-type="COI-statement"><title>Declaration of Competing Interest</title><p id="para0017">None.</p></sec></body><back><ref-list id="cebibl1"><title>References</title><ref id="bib0001"><label>1</label><element-citation publication-type="journal" id="sbref0001"><person-group person-group-type="author"><name><surname>Tang</surname><given-names>J.W.</given-names></name><name><surname>Tambyah</surname><given-names>P.A.</given-names></name><name><surname>Hui</surname><given-names>D.S.C.</given-names></name></person-group><article-title>Emergence of a novel coronavirus causing 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materials</title><p id="para0015a"><supplementary-material content-type="local-data" id="ecom0001"><media xlink:href="mmc1.pdf"><alt-text>Image, application 1</alt-text></media></supplementary-material></p></sec><ack id="ack0001"><title>Acknowledgments</title><p>We thank graduate students (Boyan Lv, Zhongyan Li, Zhongyu Chen, Yu Cheng, Mengmeng Bian, Shuang Zhang, Zuqin Zhang, and Wei Yao; all from Prof. Xinmiao Fu's research group at Fujian Normal University) for data collection. This work is support by the <funding-source id="gs0001">National Natural Science Foundation of China</funding-source> (No. 31972918 and 31770830 to XF).</p></ack><fn-group><fn id="sec0001" fn-type="supplementary-material"><p id="para0006a">Supplementary material associated with this article can be found, in the online version, at doi:<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1016/j.jinf.2020.02.019" id="interref0001">10.1016/j.jinf.2020.02.019</ext-link>.</p></fn></fn-group></back></pmc></record>Pour manipuler ce document sous Unix (Dilib)
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