High reproduction number of Middle East respiratory syndrome coronavirus in nosocomial outbreaks: mathematical modelling in Saudi Arabia and South Korea
Identifieur interne : 000E12 ( Pmc/Corpus ); précédent : 000E11; suivant : 000E13High reproduction number of Middle East respiratory syndrome coronavirus in nosocomial outbreaks: mathematical modelling in Saudi Arabia and South Korea
Auteurs : S. Choi ; E. Jung ; B. Y. Choi ; Y. J. Hur ; M. KiSource :
- The Journal of Hospital Infection [ 0195-6701 ] ; 2017.
Abstract
Effective countermeasures against emerging infectious diseases require an understanding of transmission rate and basic reproduction number (
The estimated
Url:
DOI: 10.1016/j.jhin.2017.09.017
PubMed: 28958834
PubMed Central: 7114943
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">High reproduction number of Middle East respiratory syndrome coronavirus in nosocomial outbreaks: mathematical modelling in Saudi Arabia and South Korea</title><author><name sortKey="Choi, S" sort="Choi, S" uniqKey="Choi S" first="S." last="Choi">S. Choi</name><affiliation><nlm:aff id="aff1">Department of Preventive Medicine, Hanyang University Medical College, Seoul, South Korea</nlm:aff></affiliation><affiliation><nlm:aff id="aff4">Department of Cancer Control and Population Health, Graduate School of Cancer Science and Policy, National Cancer Centre, Goyang, South Korea</nlm:aff></affiliation></author><author><name sortKey="Jung, E" sort="Jung, E" uniqKey="Jung E" first="E." last="Jung">E. Jung</name><affiliation><nlm:aff id="aff2">Department of Mathematics, Konkuk University, Seoul, South Korea</nlm:aff></affiliation></author><author><name sortKey="Choi, B Y" sort="Choi, B Y" uniqKey="Choi B" first="B. Y." last="Choi">B. Y. Choi</name><affiliation><nlm:aff id="aff1">Department of Preventive Medicine, Hanyang University Medical College, Seoul, South Korea</nlm:aff></affiliation></author><author><name sortKey="Hur, Y J" sort="Hur, Y J" uniqKey="Hur Y" first="Y. J." last="Hur">Y. J. Hur</name><affiliation><nlm:aff id="aff3">Centre for Infectious Disease Control, Korea Centre for Disease Control and Prevention, Cheongju, South Korea</nlm:aff></affiliation></author><author><name sortKey="Ki, M" sort="Ki, M" uniqKey="Ki M" first="M." last="Ki">M. Ki</name><affiliation><nlm:aff id="aff4">Department of Cancer Control and Population Health, Graduate School of Cancer Science and Policy, National Cancer Centre, Goyang, South Korea</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">28958834</idno><idno type="pmc">7114943</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7114943</idno><idno type="RBID">PMC:7114943</idno><idno type="doi">10.1016/j.jhin.2017.09.017</idno><date when="2017">2017</date><idno type="wicri:Area/Pmc/Corpus">000E12</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000E12</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">High reproduction number of Middle East respiratory syndrome coronavirus in nosocomial outbreaks: mathematical modelling in Saudi Arabia and South Korea</title><author><name sortKey="Choi, S" sort="Choi, S" uniqKey="Choi S" first="S." last="Choi">S. Choi</name><affiliation><nlm:aff id="aff1">Department of Preventive Medicine, Hanyang University Medical College, Seoul, South Korea</nlm:aff></affiliation><affiliation><nlm:aff id="aff4">Department of Cancer Control and Population Health, Graduate School of Cancer Science and Policy, National Cancer Centre, Goyang, South Korea</nlm:aff></affiliation></author><author><name sortKey="Jung, E" sort="Jung, E" uniqKey="Jung E" first="E." last="Jung">E. Jung</name><affiliation><nlm:aff id="aff2">Department of Mathematics, Konkuk University, Seoul, South Korea</nlm:aff></affiliation></author><author><name sortKey="Choi, B Y" sort="Choi, B Y" uniqKey="Choi B" first="B. Y." last="Choi">B. Y. Choi</name><affiliation><nlm:aff id="aff1">Department of Preventive Medicine, Hanyang University Medical College, Seoul, South Korea</nlm:aff></affiliation></author><author><name sortKey="Hur, Y J" sort="Hur, Y J" uniqKey="Hur Y" first="Y. J." last="Hur">Y. J. Hur</name><affiliation><nlm:aff id="aff3">Centre for Infectious Disease Control, Korea Centre for Disease Control and Prevention, Cheongju, South Korea</nlm:aff></affiliation></author><author><name sortKey="Ki, M" sort="Ki, M" uniqKey="Ki M" first="M." last="Ki">M. Ki</name><affiliation><nlm:aff id="aff4">Department of Cancer Control and Population Health, Graduate School of Cancer Science and Policy, National Cancer Centre, Goyang, South Korea</nlm:aff></affiliation></author></analytic><series><title level="j">The Journal of Hospital Infection</title><idno type="ISSN">0195-6701</idno><idno type="eISSN">1532-2939</idno><imprint><date when="2017">2017</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><title>Summary</title><sec><title>Background</title><p>Effective countermeasures against emerging infectious diseases require an understanding of transmission rate and basic reproduction number (<italic>R</italic><sub>0</sub>). <italic>R</italic><sub>0</sub> for severe acute respiratory syndrome is generally considered to be >1, whereas that for Middle East respiratory syndrome (MERS) is considered to be <1. However, this does not explain the large-scale outbreaks of MERS that occurred in Kingdom of Saudi Arabia (KSA) and South Korean hospitals.</p><p><bold><italic>Aim</italic></bold>: To estimate <italic>R</italic><sub>0</sub> in nosocomial outbreaks of MERS.</p></sec><sec><title>Methods</title><p><italic>R</italic><sub>0</sub> was estimated using the incidence decay with an exponential adjustment model. The KSA and Korean outbreaks were compared using a line listing of MERS cases compiled using publicly available sources. Serial intervals to estimate <italic>R</italic><sub>0</sub> were assumed to be six to eight days. Study parameters [<italic>R</italic><sub>0</sub> and countermeasures (<italic>d</italic>)] were estimated by fitting a model to the cumulative incidence epidemic curves using Matlab.</p></sec><sec><title>Findings</title><p>The estimated <italic>R</italic><sub>0</sub> in Korea was 3.9 in the best-fit model, with a serial interval of six days. The first outbreak cluster in a hospital in Pyeongtaek had an <italic>R</italic><sub>0</sub> of 4.04, and the largest outbreak cluster in a hospital in Samsung had an <italic>R</italic><sub>0</sub> of 5.0. Assuming a six-day serial interval, the KSA outbreaks in Jeddah and Riyadh had <italic>R</italic><sub>0</sub> values of 3.9 and 1.9, respectively.</p></sec><sec><title>Conclusion</title><p><italic>R</italic><sub>0</sub> for the nosocomial MERS outbreaks in KSA and South Korea was estimated to be in the range of 2–5, which is significantly higher than the previous estimate of <1. Therefore, more comprehensive countermeasures are needed to address these infections.</p></sec></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Chowell, G" uniqKey="Chowell G">G. Chowell</name></author><author><name sortKey="Sattenspiel, L" uniqKey="Sattenspiel L">L. Sattenspiel</name></author><author><name sortKey="Bansal, S" uniqKey="Bansal S">S. 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<front><journal-meta><journal-id journal-id-type="nlm-ta">J Hosp Infect</journal-id><journal-id journal-id-type="iso-abbrev">J. Hosp. Infect</journal-id><journal-title-group><journal-title>The Journal of Hospital Infection</journal-title></journal-title-group><issn pub-type="ppub">0195-6701</issn><issn pub-type="epub">1532-2939</issn><publisher><publisher-name>The Healthcare Infection Society. Published by Elsevier Ltd.</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">28958834</article-id><article-id pub-id-type="pmc">7114943</article-id><article-id pub-id-type="publisher-id">S0195-6701(17)30526-1</article-id><article-id pub-id-type="doi">10.1016/j.jhin.2017.09.017</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>High reproduction number of Middle East respiratory syndrome coronavirus in nosocomial outbreaks: mathematical modelling in Saudi Arabia and South Korea</article-title></title-group><contrib-group><contrib contrib-type="author" id="au1"><name><surname>Choi</surname><given-names>S.</given-names></name><xref rid="aff1" ref-type="aff">a</xref><xref rid="aff4" ref-type="aff">d</xref></contrib><contrib contrib-type="author" id="au2"><name><surname>Jung</surname><given-names>E.</given-names></name><xref rid="aff2" ref-type="aff">b</xref></contrib><contrib contrib-type="author" id="au3"><name><surname>Choi</surname><given-names>B.Y.</given-names></name><xref rid="aff1" ref-type="aff">a</xref></contrib><contrib contrib-type="author" id="au4"><name><surname>Hur</surname><given-names>Y.J.</given-names></name><xref rid="aff3" ref-type="aff">c</xref></contrib><contrib contrib-type="author" id="au5"><name><surname>Ki</surname><given-names>M.</given-names></name><email>moranki@ncc.re.kr</email><xref rid="aff4" ref-type="aff">d</xref><xref rid="cor1" ref-type="corresp">∗</xref></contrib></contrib-group><aff id="aff1"><label>a</label>Department of Preventive Medicine, Hanyang University Medical College, Seoul, South Korea</aff><aff id="aff2"><label>b</label>Department of Mathematics, Konkuk University, Seoul, South Korea</aff><aff id="aff3"><label>c</label>Centre for Infectious Disease Control, Korea Centre for Disease Control and Prevention, Cheongju, South Korea</aff><aff id="aff4"><label>d</label>Department of Cancer Control and Population Health, Graduate School of Cancer Science and Policy, National Cancer Centre, Goyang, South Korea</aff><author-notes><corresp id="cor1"><label>∗</label>Corresponding author. Address: Department of Cancer Control and Policy, Graduate School of Cancer Science and Policy, National Cancer Centre, 323 Ilsan-ro, Ilsandong-gu, Goyang 10408, South Korea. Tel.: +82 31 920 2736; fax: +82 2 6455 8699. <email>moranki@ncc.re.kr</email></corresp></author-notes><pub-date pub-type="pmc-release"><day>25</day><month>9</month><year>2017</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>6</month><year>2018</year></pub-date><pub-date pub-type="epub"><day>25</day><month>9</month><year>2017</year></pub-date><volume>99</volume><issue>2</issue><fpage>162</fpage><lpage>168</lpage><history><date date-type="received"><day>4</day><month>7</month><year>2017</year></date><date date-type="accepted"><day>20</day><month>9</month><year>2017</year></date></history><permissions><copyright-statement>© 2017 The Healthcare Infection Society. Published by Elsevier Ltd. All rights reserved.</copyright-statement><copyright-year>2017</copyright-year><copyright-holder>The Healthcare Infection Society</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 id="abs0010"><title>Summary</title><sec><title>Background</title><p>Effective countermeasures against emerging infectious diseases require an understanding of transmission rate and basic reproduction number (<italic>R</italic><sub>0</sub>). <italic>R</italic><sub>0</sub> for severe acute respiratory syndrome is generally considered to be >1, whereas that for Middle East respiratory syndrome (MERS) is considered to be <1. However, this does not explain the large-scale outbreaks of MERS that occurred in Kingdom of Saudi Arabia (KSA) and South Korean hospitals.</p><p><bold><italic>Aim</italic></bold>: To estimate <italic>R</italic><sub>0</sub> in nosocomial outbreaks of MERS.</p></sec><sec><title>Methods</title><p><italic>R</italic><sub>0</sub> was estimated using the incidence decay with an exponential adjustment model. The KSA and Korean outbreaks were compared using a line listing of MERS cases compiled using publicly available sources. Serial intervals to estimate <italic>R</italic><sub>0</sub> were assumed to be six to eight days. Study parameters [<italic>R</italic><sub>0</sub> and countermeasures (<italic>d</italic>)] were estimated by fitting a model to the cumulative incidence epidemic curves using Matlab.</p></sec><sec><title>Findings</title><p>The estimated <italic>R</italic><sub>0</sub> in Korea was 3.9 in the best-fit model, with a serial interval of six days. The first outbreak cluster in a hospital in Pyeongtaek had an <italic>R</italic><sub>0</sub> of 4.04, and the largest outbreak cluster in a hospital in Samsung had an <italic>R</italic><sub>0</sub> of 5.0. Assuming a six-day serial interval, the KSA outbreaks in Jeddah and Riyadh had <italic>R</italic><sub>0</sub> values of 3.9 and 1.9, respectively.</p></sec><sec><title>Conclusion</title><p><italic>R</italic><sub>0</sub> for the nosocomial MERS outbreaks in KSA and South Korea was estimated to be in the range of 2–5, which is significantly higher than the previous estimate of <1. Therefore, more comprehensive countermeasures are needed to address these infections.</p></sec></abstract><kwd-group id="kwrds0010"><title>Keywords</title><kwd>Nosocomial infection</kwd><kwd>Basic reproduction number</kwd><kwd>Epidemiology</kwd><kwd>Middle east respiratory syndrome coronavirus</kwd><kwd>Mathematical modelling</kwd><kwd>South Korea</kwd></kwd-group></article-meta></front><body><sec id="sec1"><title>Introduction</title><p id="p0010">The emergence of infectious diseases associated with Middle East respiratory syndrome (MERS), severe acute respiratory syndrome and Ebola has created unprecedented public health challenges. These challenges are complicated by the lack of basic epidemiological data, which makes it difficult to predict epidemics. Thus, it is important to quantify actual outbreaks as novel infectious diseases emerge. Disease severity and rate of transmission can be predicted by mathematical models using the basic reproduction number (<italic>R</italic><sub>0</sub>) <xref rid="bib1" ref-type="bibr">[1]</xref>. For example, <italic>R</italic><sub>0</sub> has been used extensively to assess pathogen transmissibility, outbreak severity and epidemiological control <xref rid="bib2" ref-type="bibr">[2]</xref>, <xref rid="bib3" ref-type="bibr">[3]</xref>, <xref rid="bib4" ref-type="bibr">[4]</xref>.</p><p id="p0015">In previous studies, <italic>R</italic><sub>0</sub> for MERS has ranged from 0.42 to 0.92 <xref rid="bib5" ref-type="bibr">[5]</xref>, <xref rid="bib6" ref-type="bibr">[6]</xref>, <xref rid="bib7" ref-type="bibr">[7]</xref>, <xref rid="bib8" ref-type="bibr">[8]</xref>, which suggests that the MERS coronavirus (MERS-CoV) has limited transmissibility. However, these studies typically considered community-acquired MERS infections. In this context, nosocomial infections can exhibit different <italic>R</italic><sub>0</sub> values as the transmission routes for community-acquired and nosocomial infections often differ <xref rid="bib9" ref-type="bibr">[9]</xref>. Recent studies have examined large nosocomial outbreaks of MERS-CoV infection in Jeddah and Riyadh within the Kingdom of Saudi Arabia (KSA). One study reported higher nosocomial <italic>R</italic><sub>0</sub> values than those from community-acquired infections when using the incidence decay with exponential adjustment (IDEA) model, which yielded values of 3.5–6.7 in Jeddah and 2.0–2.8 in Riyadh <xref rid="bib10" ref-type="bibr">[10]</xref>. The IDEA model is simple because it does not consider the population-level immune status, which makes it especially useful for modelling emerging infectious diseases in resource-limited settings.</p><p id="p0020">The MERS outbreak in South Korea was associated with nosocomial infections. At that time, the Korea Centre for Disease Control and Prevention (KCDC) assumed that the outbreak had an <italic>R</italic><sub>0</sub> <1. Thus, the initial countermeasures were not sufficiently aggressive to prevent the spread of MERS-CoV infection to other hospitals. Therefore, the IDEA model was used to evaluate and compare the MERS <italic>R</italic><sub>0</sub> values from the outbreaks in both KSA and South Korean hospitals.</p></sec><sec id="sec2"><title>Methods</title><sec id="sec2.1"><title>Data source</title><p id="p0025">KSA data were obtained using a line listing of MERS-CoV cases that was maintained by Andrew Rambaut (updated on 19<sup>th</sup> August 2015). The line listing was created using data from the KSA Ministry of Health and World Health Organization (WHO) report <xref rid="bib10" ref-type="bibr">[10]</xref>. Since only 44% of cases in the KSA listing included the onset date, hospitalization dates or reported dates were used instead. The Korean data were obtained from the KCDC. Among the 186 MERS cases, 178 had confirmed onset dates. The eight cases with unknown onset dates were assigned dates based on laboratory confirmation. All cases in KSA and Korea were confirmed based on laboratory findings. Study parameters [<italic>R</italic><sub>0</sub> and countermeasures (<italic>d</italic>)] were estimated by fitting a model to the cumulative incidence epidemic curves using Matlab (Mathworks, Natick, MA, USA).</p><p id="p0030">The data were narrowed down to the nosocomial cases alone. Cases with unknown transmissions were considered to be nosocomial if: (a) the patient was in contact with a healthcare worker and/or hospitalized patients; or (b) the patient was a healthcare worker. Cases were excluded if they could not be verified as nosocomial (e.g. zoonotic transmission, family contact or community infection).</p></sec><sec id="sec2.2"><title>Model</title><p id="p0035">The IDEA model was used to estimate <italic>R</italic><sub>0</sub> as reported previously <xref rid="bib11" ref-type="bibr">[11]</xref>, together with publicly available data. The IDEA model is based on the concept that the number of incident cases (<inline-formula><mml:math id="M1" altimg="si1.gif" overflow="scroll"><mml:mi>I</mml:mi></mml:math></inline-formula>) in an epidemic generation (<inline-formula><mml:math id="M2" altimg="si2.gif" overflow="scroll"><mml:mi>t</mml:mi></mml:math></inline-formula>) can be counted as:<disp-formula id="fd1"><label>(1)</label><mml:math id="M3" display="block" altimg="si3.gif" overflow="scroll"><mml:mrow><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msubsup><mml:mi>R</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mspace width="0.25em"></mml:mspace></mml:mrow><mml:mrow><mml:mspace width="0.25em"></mml:mspace><mml:mi>t</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math></disp-formula>when an outbreak occurs, epidemic control measures can be implemented, which can, in turn, change <italic>R</italic><sub>0</sub>. Therefore, the relationship between <italic>I</italic> and <italic>R</italic><sub>0</sub> with <inline-formula><mml:math id="M4" altimg="si4.gif" overflow="scroll"><mml:mi>d</mml:mi></mml:math></inline-formula> is defined as follows:<disp-formula id="fd2"><label>(2)</label><mml:math id="M5" display="block" altimg="si5.gif" overflow="scroll"><mml:mrow><mml:mi>I</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>R</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msup><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>d</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>t</mml:mi></mml:msup></mml:mrow></mml:mfrac></mml:mrow><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mi>t</mml:mi></mml:msup></mml:mrow></mml:math></disp-formula></p><p id="p0040"><italic>R</italic><sub>0</sub> and <italic>d</italic> are estimated by fitting <inline-formula><mml:math id="M6" altimg="si1.gif" overflow="scroll"><mml:mi>I</mml:mi></mml:math></inline-formula> from Eq. <xref rid="fd2" ref-type="disp-formula">(2)</xref> to the observed cumulative incidence data of MERS using the least-squares data-fitting method. Since the IDEA model is parameterized using epidemic generation time, incidence case counts were aggregated at serial intervals of six, seven and eight days in the present study <xref rid="bib10" ref-type="bibr">[10]</xref>.</p><p id="p0045">Two large outbreaks were considered in each country studied: the outbreaks in Riyadh and Jeddah for KSA; and those in Pyeongtaek St. Mary's Hospital and Samsung Seoul Hospital for South Korea. The term ‘resnorm’ is defined as the norm of the residual, which is the squared 2-norm of the residual; it measures the difference between observed data and the fitted value provided by a model. However, as residuals can be positive or negative, a sum of residuals is not a good measure of overall error in the fit. Therefore, a better measure of error is the sum of the squared residuals (<inline-formula><mml:math id="M7" altimg="si6.gif" overflow="scroll"><mml:mtext>E</mml:mtext></mml:math></inline-formula>), which is calculated as follows:<disp-formula id="fd3"><label>(3)</label><mml:math id="M8" display="block" altimg="si7.gif" overflow="scroll"><mml:mrow><mml:mtext>E</mml:mtext><mml:mo>=</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:munder><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>x</mml:mi><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mi>y</mml:mi><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow></mml:mrow></mml:math></disp-formula></p><p id="p0050">The functions to be fit were the given input data (xdata), the observed output data, (ydata) and F(x, xdata), where xdata was an epidemic generation, ydata was the observed cumulative incidence data, and F(x, xdata) was Eq. <xref rid="fd2" ref-type="disp-formula">(2)</xref>.</p><p id="p0055">Since the generation times and the estimated values differ according to serial interval times, resnorm changes accordingly. Therefore, to compare resnorm with the serial interval time, relative resnorm was defined as follows:<disp-formula id="fd4"><label>(4)</label><mml:math id="M9" display="block" altimg="si8.gif" overflow="scroll"><mml:mrow><mml:mtext>E</mml:mtext><mml:mo>=</mml:mo><mml:munder><mml:mo>∑</mml:mo><mml:mi>i</mml:mi></mml:munder><mml:mrow><mml:mfrac><mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>x</mml:mi><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>−</mml:mo><mml:mi>y</mml:mi><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mn>2</mml:mn></mml:msup></mml:mrow><mml:mrow><mml:mi>y</mml:mi><mml:mi>d</mml:mi><mml:mi>a</mml:mi><mml:mi>t</mml:mi><mml:msub><mml:mi>a</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:mrow></mml:math></disp-formula></p><p id="p0060">The IDEA model was fitted to the cumulative South Korean MERS-CoV case data from the onset date of the first case to the onset date of the last case. The outbreak start date was defined as 11<sup>th</sup> May 2015 because that was the symptom onset date for Patient 0, who was the index case and caused the outbreak in the Pyeongtaek hospital. Patient 14 caused the outbreak at the Samsung hospital, and his symptom onset date was 21<sup>st</sup> May 2015. The last case of the MERS outbreak in South Korea was observed on 4<sup>th</sup> July 2015. The KSA MERS outbreak model was fitted using the cumulative incidence data from 28<sup>th</sup> March 2014 to 2<sup>nd</sup> June 2014 in Jeddah, and from 20<sup>th</sup> March 2014 to 29<sup>th</sup> May 2014 in Riyadh.</p></sec><sec id="sec2.3"><title>Ethical considerations</title><p id="p0065">All data used in these analyses were de-identified publicly available data obtained from WHO, the KSA Ministry of Health website or KCDC datasets. As such, these data were deemed to be exempt from institutional review board assessment.</p></sec></sec><sec id="sec3"><title>Results</title><p id="p0070">KSA outbreaks were relatively large, with 180 cases (over the course of 67 days) in Jeddah and 142 cases (over the course of 71 days) in Riyadh. The Korean outbreaks involved 186 cases (over the course of 55 days), including 36 cases (over the course of 23 days) in the Pyeongtaek hospital and 91 cases (over the course of 45 days) in the Samsung hospital. Most Korean cases (180) were nosocomial, with the exception of four cases acquired by household transmission and two cases with unknown modes of transmission. In KSA, only two cases involved confirmed zoonotic transmission, while a large number of unknown transmissions (Jeddah: 99 cases; Riyadh: 69 cases) and hospital exposures (Jeddah: 80 cases; Riyadh: 70 cases) were observed (<xref rid="tbl1" ref-type="table">Table I</xref>).<table-wrap position="float" id="tbl1"><label>Table I</label><caption><p>Characteristics of selected Middle East respiratory syndrome (MERS) outbreaks in Saudi Arabia and South Korea</p></caption><table frame="hsides" rules="groups"><thead><tr><th colspan="2" rowspan="2"></th><th colspan="2">Saudi Arabia<hr></hr></th><th colspan="3">South Korea<hr></hr></th></tr><tr><th>Jeddah</th><th>Riyadh</th><th>Total</th><th>Pyeongtaek St. Mary's hospital</th><th>Samsung Seoul hospital</th></tr></thead><tbody><tr><td>Outbreak</td><td>Onset date</td><td align="char">28/03/2014</td><td align="char">20/03/2014</td><td align="char">11/05/2015</td><td align="char">15/05/2015</td><td align="char">25/05/2015</td></tr><tr><td></td><td>Duration (day)</td><td align="char">67</td><td align="char">71</td><td align="char">55</td><td align="char">23</td><td align="char">45</td></tr><tr><td></td><td>No. of cases</td><td align="char">180</td><td align="char">142</td><td align="char">186</td><td align="char">36</td><td align="char">91</td></tr><tr><td>Exposure</td><td>Nosocomial</td><td align="char">80<xref rid="tbl1fna" ref-type="table-fn">a</xref></td><td align="char">70<xref rid="tbl1fna" ref-type="table-fn">a</xref></td><td align="char">180</td><td align="char">36</td><td align="char">88</td></tr><tr><td></td><td>Household</td><td></td><td></td><td align="char">4</td><td align="char">0</td><td align="char">3</td></tr><tr><td></td><td>Zoonotic</td><td align="char">1</td><td align="char">1</td><td align="char">0</td><td align="char">0</td><td align="char">0</td></tr><tr><td></td><td>Unknown</td><td align="char">99</td><td align="char">69</td><td align="char">2</td><td align="char">0</td><td align="char">0</td></tr><tr><td>Status<xref rid="tbl1fnb" ref-type="table-fn">b</xref></td><td>Healthcare worker</td><td align="char">40</td><td align="char">8</td><td align="char">39</td><td align="char">3</td><td align="char">15</td></tr><tr><td></td><td>Patient</td><td></td><td></td><td align="char">82</td><td align="char">20</td><td align="char">36</td></tr><tr><td></td><td>Family or visitor</td><td></td><td></td><td align="char">63</td><td align="char">13</td><td align="char">40</td></tr><tr><td></td><td>Unknown</td><td align="char">140</td><td align="char">134</td><td align="char">2</td><td align="char">0</td><td align="char">0</td></tr><tr><td>Date<xref rid="tbl1fnc" ref-type="table-fn">c</xref></td><td>Onset date</td><td align="char">75</td><td align="char">66</td><td align="char">178</td><td align="char">36</td><td align="char">85</td></tr><tr><td></td><td>Hospitalized date</td><td align="char">85</td><td align="char">79</td><td align="char">186</td><td align="char">36</td><td align="char">91</td></tr><tr><td></td><td>Reported date</td><td align="char">180</td><td align="char">142</td><td align="char">186</td><td align="char">36</td><td align="char">91</td></tr></tbody></table><table-wrap-foot><fn id="tbl1fna"><label>a</label><p id="ntpara0010">Nosocomial cases included healthcare workers and individuals who were in contact with a healthcare worker or hospitalized patients.</p></fn></table-wrap-foot><table-wrap-foot><fn id="tbl1fnb"><label>b</label><p id="ntpara0015">The status of cases when they were exposed to MERS.</p></fn></table-wrap-foot><table-wrap-foot><fn id="tbl1fnc"><label>c</label><p id="ntpara0020">The number of cases with information for onset date, hospitalization date and reported date of MERS.</p></fn></table-wrap-foot></table-wrap></p><p id="p0075">The IDEA model was fitted to the daily KSA and Korea MERS-CoV case data according to the onset date. <xref rid="fig1" ref-type="fig">Figure 1</xref>displays the cumulative MERS-CoV case data for the 2014 KSA and the 2015 South Korea MERS outbreaks. The date of symptom onset for Patient 0 was 11<sup>th</sup> May 2015; however, he was admitted to the Pyeongtaek hospital on 15<sup>th</sup> May 2015. Therefore, the outbreak was assumed to start on 15<sup>th</sup> May 2015 via a simulation of the Pyeongtaek hospital outbreak. The outbreak start date for the Samsung hospital was determined to be 25<sup>th</sup> May 2015, following the same logic (<xref rid="fig1" ref-type="fig">Figure 1</xref>).<fig id="fig1"><label>Figure 1</label><caption><p>Epidemic curves of cumulative cases by selected Middle East respiratory syndrome outbreaks in (a) Saudi Arabia (red circles, Jeddah; blue asterisks, Riyadh) and (b) South Korea (green squares, total; red circles, Pyeongtaek; blue asterisks, Samsung).</p></caption><graphic xlink:href="gr1_lrg"></graphic></fig></p><p id="p0080"><xref rid="fig2" ref-type="fig">Figure 2</xref>shows the results of the 2014 KSA outbreak. Squares, circles and asterisks represent data aggregation of the number of cases by serial intervals of six, seven and eight days, respectively; the curves represent model fits for best-fit parameters. The estimated <italic>R</italic><sub>0</sub> values for Jeddah and Riyadh were in the range of 3.95–6.68 and 1.92–2.52, respectively, using serial intervals of six to eight days. The estimated <italic>R</italic><sub>0</sub> values for the Korea MERS outbreak were 3.96, 4.91 and 5.95 for serial intervals of six, seven and eight days, respectively (<xref rid="fig3" ref-type="fig">Figure 3</xref>). Since most cases were related to nosocomial infections, <italic>R</italic><sub>0</sub> for each hospital was also considered. The outbreak in the Samsung hospital was larger than that in the Pyeongtaek hospital (the first Korean outbreak). The Pyeongtaek hospital exhibited best-fit <italic>R</italic><sub>0</sub> values of 4.04, 4.23 and 4.39 for serial intervals of six, seven and eight days, respectively, while the Samsung hospital exhibited greater <italic>R</italic><sub>0</sub> values of 5.0, 6.8 and 8.11 for serial intervals of six, seven and eight days, respectively. <xref rid="fig3" ref-type="fig">Figure 3</xref> shows that the IDEA model provided well-fitted curves for the cumulative data regarding South Korean MERS symptom-onset dates for all cases.<fig id="fig2"><label>Figure 2</label><caption><p>Best-fit reproduction number (<italic>R</italic><sub>0</sub>) by serial intervals of Middle East respiratory syndrome in Jeddah and Riyadh, Saudi Arabia, 2014, using the incidence decay with exponential adjustment model. Red squares, Jeddah, six days; red circles, Jeddah, seven days; red asterisks, Jeddah, eight days; blue squares, Riyadh, six days; blue circles, Riyadh, seven days; blue asterisks, Riyadh, eight days.</p></caption><graphic xlink:href="gr2_lrg"></graphic></fig><fig id="fig3"><label>Figure 3</label><caption><p>Best-fit reproduction number (<italic>R</italic><sub>0</sub>) by serial intervals of Middle East respiratory syndrome in South Korea, 2015, using the incidence decay with exponential adjustment model. Green squares, total, six days; green circles, total, seven days; green asterisks, total, eight days; red squares, Pyeongtaek, six days; red circles, Pyeongtaek, seven days; red asterisks, Pyeongtaek, eight days; blue squares, Samsung, six days; blue circles, Samsung, seven days; blue asterisks, Samsung, eight days.</p></caption><graphic xlink:href="gr3_lrg"></graphic></fig></p><p id="p0085">Although the IDEA model seemed to be appropriate, the original data never fit the model precisely. Therefore, the appropriateness of the model was assessed. Error was evaluated using the relative resnorm to find the best-fit parameters. The results indicated that the best-fit <italic>R</italic><sub>0</sub> and serial interval values were 4.9 and seven days for all cases, 4.39 and eight days for the Pyeongtaek hospital, and 5.0 and six days for the Samsung hospital, respectively. <italic>d</italic> increased with each serial interval because the daily effort of <italic>d</italic> was aggregated by serial interval.</p></sec><sec id="sec4"><title>Discussion</title><p id="p0090">The clusters of MERS-CoV cases in KSA healthcare facilities occurred from late March to late May 2014, while the Korean outbreaks occurred from mid-May to early July 2015. These hospital-based outbreaks exhibited characteristics different from those of community-based outbreaks (higher <italic>R</italic><sub>0</sub> values and case fatality rates) <xref rid="bib12" ref-type="bibr">[12]</xref>, <xref rid="bib13" ref-type="bibr">[13]</xref>.</p><p id="p0095">The estimated <italic>R</italic><sub>0</sub> is a basic epidemiological variable that is important for selecting appropriate countermeasure efforts. However, an emerging infectious disease often has unknown epidemiology, making it difficult to model mathematically. Several methods have been proposed to address this issue, including the IDEA model. The Richards model can also estimate <italic>R</italic><sub>0</sub> using the cumulative daily number of cases and the outbreak turning point (or the peak, <inline-formula><mml:math id="M10" altimg="si9.gif" overflow="scroll"><mml:mrow><mml:msub><mml:mi>t</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:math></inline-formula>) <xref rid="bib14" ref-type="bibr">[14]</xref>. In this context, Hsieh used the Richards model to estimate <italic>R</italic><sub>0</sub> values for the Korean outbreak as 7.0–19.3. However, the Richards model does not consider any countermeasures implemented during an outbreak; therefore, it can only be used after an outbreak has peaked.</p><p id="p0100">The present study used the IDEA model to estimate <italic>R</italic><sub>0</sub> values from the MERS outbreaks in KSA and South Korea. The IDEA model exhibited a good fit: the estimated <italic>R</italic><sub>0</sub> values for South Korea were 3.9–8.0, and the best-fit <italic>R</italic><sub>0</sub> was 4.9 for a serial interval of seven days. Conversely, <italic>R</italic><sub>0</sub> values for Riyadh and Jeddah were 1.9–2.5 and 3.9–6.9, respectively, using serial intervals of six to eight days. Majumder <italic>et al.</italic><xref rid="bib10" ref-type="bibr">[10]</xref> used the IDEA model and estimated very similar <italic>R</italic><sub>0</sub> values of 2.0–2.8 for Riyadh and 3.5–6.7 for Jeddah, with serial intervals of six to eight days. However, the estimated <italic>R</italic><sub>0</sub> values from the present study were much higher than the previously reported values of <1 for MERS (the threshold for an epidemic) <xref rid="bib15" ref-type="bibr">[15]</xref>. Regardless, the Korean Government assumed that the outbreak had an <italic>R</italic><sub>0</sub> value <1 based on the previous research. The initial criterion for quarantine, therefore, was limited to cases of ‘close contacts’, which were defined as people who were within 2 m of a MERS patient for ≥1 h <xref rid="bib16" ref-type="bibr">[16]</xref>. These quarantines – established using an incorrectly assumed <italic>R</italic><sub>0</sub> – resulted in more MERS patients and greater hospital-to-hospital transmission <xref rid="bib16" ref-type="bibr">[16]</xref>.</p><p id="p0105">A serial interval is the interval between successive cases of an infectious disease. This time period depends on the temporal relationship between the infectiousness of the disease, the clinical onset of the source case, and the incubation period of the receiving case <xref rid="bib17" ref-type="bibr">[17]</xref>. As MERS becomes infectious with the onset of clinical symptoms, the MERS latency period equals the incubation period. Therefore, the shortest serial interval could be the same as the incubation period, and the longest serial interval could be the sum of the incubation period and the maximum duration of infectiousness. During the Korean MERS outbreak, several super-spreading events occurred because the MERS cases were not isolated immediately upon presentation of clinical symptoms <xref rid="bib18" ref-type="bibr">[18]</xref>. Thus, these cases contacted susceptible individuals for up to one week after the onset of their clinical symptoms. However, most MERS cases with laboratory confirmation were isolated immediately after onset of clinical symptoms <xref rid="bib19" ref-type="bibr">[19]</xref>, <xref rid="bib20" ref-type="bibr">[20]</xref>. In this study, as the incubation period was two to 14 days (median: six days), the serial interval was slightly longer than the incubation period. The IDEA model with several serial intervals (four to 12 days) was used and found that intervals of six to eight days provided the best fit. For KSA data, even though the reported date was used instead of the onset date, <italic>R</italic><sub>0</sub> was not affected because aggregated data by serial intervals was used in the analysis.</p><p id="p0110">The IDEA model is limited by the fact that <italic>d</italic> cannot be compared with <italic>d</italic> of another model. In this context, an increasing <italic>d</italic> in accordance with increasing serial intervals indicates that the countermeasure efforts are increasing. However, the size of <italic>d</italic> cannot be compared between two or more models of different outbreaks. Nevertheless, the strength of the IDEA model is its simplicity because <italic>R</italic><sub>0</sub> can be estimated using the cumulative number of cases according to the serial interval alone.</p><p id="p0115">In conclusion, the estimated <italic>R</italic><sub>0</sub> values from the KSA outbreaks (Riyadh and Jeddah) ranged from 1.9 to 6.9, whereas the estimated values from the South Korean outbreaks ranged from 3.9 to 8.0. Based on these findings, it appears that nosocomial MERS-CoV outbreaks in KSA and South Korea had higher <italic>R</italic><sub>0</sub> values than the previously assumed values of <1. Although community-acquired infections are caused by contact, nosocomial infections are caused by a combination of contact and aerosol transmission; therefore, <italic>R</italic><sub>0</sub> values for nosocomial infections can be higher than those for community-acquired infections. Hence, more comprehensive countermeasures are needed to address nosocomial MERS infections and prevent spread.</p></sec><sec id="sec5"><title>Conflict of interest statement</title><p id="p0120">None declared.</p></sec><sec id="sec6"><title>Funding source</title><p id="p0125">This work was supported by the <funding-source id="gs1">National Cancer Center</funding-source> Grant (NCC-1710141-1) and the <funding-source id="gs2">Korea National Research Foundation</funding-source> Grant (NRF-2015R1A6A3A01020594).</p></sec><sec sec-type="data-availability" id="sec7"><title>Data availability</title><p id="p0130">All relevant data are available at <ext-link ext-link-type="uri" xlink:href="http://rambaut.github.io/MERS-Tools/cases2.html" id="intref0010">http://rambaut.github.io/MERS-Tools/cases2.html</ext-link>.</p></sec></body><back><ref-list id="cebib0010"><title>References</title><ref id="bib1"><label>1</label><element-citation publication-type="journal" id="sref1"><person-group 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