Effects of Timely Control Intervention on the Spread of Middle East Respiratory Syndrome Coronavirus Infection
Identifieur interne : 000972 ( Pmc/Corpus ); précédent : 000971; suivant : 000973Effects of Timely Control Intervention on the Spread of Middle East Respiratory Syndrome Coronavirus Infection
Auteurs : Ilsu Choi ; Dong Ho Lee ; Yongkuk KimSource :
- Osong Public Health and Research Perspectives [ 2210-9099 ] ; 2017.
Abstract
The 2015 Middle East Respiratory Syndrome Coronavirus (MERS-CoV) outbreak in Korea caused major economic and social problems. The control intervention was conducted during the MERS-CoV outbreak in Korea immediately after the confirmation of the index case. This study investigates whether the early risk communication with the general public and mass media is an effective preventive strategy.
The SEIR (Susceptible, Exposed, Infectious, Recovered) model with estimated parameters for the time series data of the daily MERS-CoV incidence in Korea was considered from May to December 2015. For 10,000 stochastic simulations, the SEIR model was computed using the Gillespie algorithm. Depending on the time of control intervention on the 20th, 40th, and 60th days after the identification of the index case, the box plots of MERS-CoV incidences in Korea were computed, and the results were analyzed via ANOVA.
The box plots showed that there was a significant difference between the non-intervention and intervention groups (the 20th day, 40th day, and 60th day groups) and seemed to show no significant difference based on the time of intervention. However, the ANOVA revealed that early intervention was a good strategy to control the disease.
Appropriate risk communication can secure the confidence of the general public in the public health authorities.
Url:
DOI: 10.24171/j.phrp.2017.8.6.03
PubMed: 29354394
PubMed Central: 5749487
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Effects of Timely Control Intervention on the Spread of Middle East Respiratory Syndrome Coronavirus Infection</title><author><name sortKey="Choi, Ilsu" sort="Choi, Ilsu" uniqKey="Choi I" first="Ilsu" last="Choi">Ilsu Choi</name><affiliation><nlm:aff id="af1-phrp-08-373">Department of Statistics, Chonnam National University, Gwangju, Korea</nlm:aff></affiliation></author><author><name sortKey="Lee, Dong Ho" sort="Lee, Dong Ho" uniqKey="Lee D" first="Dong Ho" last="Lee">Dong Ho Lee</name><affiliation><nlm:aff id="af2-phrp-08-373">Department of Mathematics, Kyungpook National University, Daegu, Korea</nlm:aff></affiliation></author><author><name sortKey="Kim, Yongkuk" sort="Kim, Yongkuk" uniqKey="Kim Y" first="Yongkuk" last="Kim">Yongkuk Kim</name><affiliation><nlm:aff id="af2-phrp-08-373">Department of Mathematics, Kyungpook National University, Daegu, Korea</nlm:aff></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">29354394</idno><idno type="pmc">5749487</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5749487</idno><idno type="RBID">PMC:5749487</idno><idno type="doi">10.24171/j.phrp.2017.8.6.03</idno><date when="2017">2017</date><idno type="wicri:Area/Pmc/Corpus">000972</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000972</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Effects of Timely Control Intervention on the Spread of Middle East Respiratory Syndrome Coronavirus Infection</title><author><name sortKey="Choi, Ilsu" sort="Choi, Ilsu" uniqKey="Choi I" first="Ilsu" last="Choi">Ilsu Choi</name><affiliation><nlm:aff id="af1-phrp-08-373">Department of Statistics, Chonnam National University, Gwangju, Korea</nlm:aff></affiliation></author><author><name sortKey="Lee, Dong Ho" sort="Lee, Dong Ho" uniqKey="Lee D" first="Dong Ho" last="Lee">Dong Ho Lee</name><affiliation><nlm:aff id="af2-phrp-08-373">Department of Mathematics, Kyungpook National University, Daegu, Korea</nlm:aff></affiliation></author><author><name sortKey="Kim, Yongkuk" sort="Kim, Yongkuk" uniqKey="Kim Y" first="Yongkuk" last="Kim">Yongkuk Kim</name><affiliation><nlm:aff id="af2-phrp-08-373">Department of Mathematics, Kyungpook National University, Daegu, Korea</nlm:aff></affiliation></author></analytic><series><title level="j">Osong Public Health and Research Perspectives</title><idno type="ISSN">2210-9099</idno><idno type="eISSN">2233-6052</idno><imprint><date when="2017">2017</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><sec><title>Objectives</title><p>The 2015 Middle East Respiratory Syndrome Coronavirus (MERS-CoV) outbreak in Korea caused major economic and social problems. The control intervention was conducted during the MERS-CoV outbreak in Korea immediately after the confirmation of the index case. This study investigates whether the early risk communication with the general public and mass media is an effective preventive strategy.</p></sec><sec><title>Methods</title><p>The SEIR (Susceptible, Exposed, Infectious, Recovered) model with estimated parameters for the time series data of the daily MERS-CoV incidence in Korea was considered from May to December 2015. For 10,000 stochastic simulations, the SEIR model was computed using the Gillespie algorithm. Depending on the time of control intervention on the 20th, 40th, and 60th days after the identification of the index case, the box plots of MERS-CoV incidences in Korea were computed, and the results were analyzed via ANOVA.</p></sec><sec><title>Results</title><p>The box plots showed that there was a significant difference between the non-intervention and intervention groups (the 20th day, 40th day, and 60th day groups) and seemed to show no significant difference based on the time of intervention. However, the ANOVA revealed that early intervention was a good strategy to control the disease.</p></sec><sec><title>Conclusion</title><p>Appropriate risk communication can secure the confidence of the general public in the public health authorities.</p></sec></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Hsieh, Yh" uniqKey="Hsieh Y">YH Hsieh</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Kim, Y" uniqKey="Kim Y">Y Kim</name></author><author><name sortKey="Lee, S" uniqKey="Lee S">S Lee</name></author><author><name sortKey="Chu, C" uniqKey="Chu C">C Chu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lee, J" uniqKey="Lee J">J Lee</name></author><author><name sortKey="Chowell, G" uniqKey="Chowell G">G Chowell</name></author><author><name sortKey="Jung, E" uniqKey="Jung E">E Jung</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mizumoto, K" uniqKey="Mizumoto K">K Mizumoto</name></author><author><name sortKey="Saitoh, M" uniqKey="Saitoh M">M Saitoh</name></author><author><name sortKey="Chowell, G" uniqKey="Chowell G">G Chowell</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Park, Hy" uniqKey="Park H">HY Park</name></author><author><name sortKey="Lee, Ej" uniqKey="Lee E">EJ Lee</name></author><author><name sortKey="Ryu, Yw" uniqKey="Ryu Y">YW Ryu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Stone, L" uniqKey="Stone L">L Stone</name></author><author><name sortKey="Shulgin, B" uniqKey="Shulgin B">B Shulgin</name></author><author><name sortKey="Agur, Z" uniqKey="Agur Z">Z Agur</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Virlogeux, V" uniqKey="Virlogeux V">V Virlogeux</name></author><author><name sortKey="Fang, Vj" uniqKey="Fang V">VJ Fang</name></author><author><name sortKey="Park, M" uniqKey="Park M">M Park</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Virlogeux, V" uniqKey="Virlogeux V">V Virlogeux</name></author><author><name sortKey="Park, M" uniqKey="Park M">M Park</name></author><author><name sortKey="Wu, Jt" uniqKey="Wu J">JT Wu</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Xia, Zq" uniqKey="Xia Z">ZQ Xia</name></author><author><name sortKey="Zhang, J" uniqKey="Zhang J">J Zhang</name></author><author><name sortKey="Xue, Yk" uniqKey="Xue Y">YK Xue</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Lee, Dh" uniqKey="Lee D">DH Lee</name></author><author><name sortKey="Masud, Ma" uniqKey="Masud M">MA Masud</name></author><author><name sortKey="Kim, Bn" uniqKey="Kim B">BN Kim</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Gillespie, Dt" uniqKey="Gillespie D">DT Gillespie</name></author></analytic></biblStruct></listBibl></div1></back></TEI><pmc article-type="research-article"><pmc-dir>properties open_access</pmc-dir>
<front><journal-meta><journal-id journal-id-type="nlm-ta">Osong Public Health Res Perspect</journal-id><journal-id journal-id-type="iso-abbrev">Osong Public Health Res Perspect</journal-id><journal-id journal-id-type="publisher-id">kphrp1</journal-id><journal-title-group><journal-title>Osong Public Health and Research Perspectives</journal-title></journal-title-group><issn pub-type="ppub">2210-9099</issn><issn pub-type="epub">2233-6052</issn><publisher><publisher-name>Korea Centers for Disease Control and Prevention</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">29354394</article-id><article-id pub-id-type="pmc">5749487</article-id><article-id pub-id-type="doi">10.24171/j.phrp.2017.8.6.03</article-id><article-id pub-id-type="publisher-id">phrp-08-373</article-id><article-categories><subj-group subj-group-type="heading"><subject>Original Article</subject></subj-group></article-categories><title-group><article-title>Effects of Timely Control Intervention on the Spread of Middle East Respiratory Syndrome Coronavirus Infection</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Choi</surname><given-names>Ilsu</given-names></name><xref ref-type="aff" rid="af1-phrp-08-373">a</xref></contrib><contrib contrib-type="author"><name><surname>Lee</surname><given-names>Dong Ho</given-names></name><xref ref-type="aff" rid="af2-phrp-08-373">b</xref></contrib><contrib contrib-type="author"><name><surname>Kim</surname><given-names>Yongkuk</given-names></name><xref ref-type="aff" rid="af2-phrp-08-373">b</xref><xref ref-type="corresp" rid="c1-phrp-08-373"></xref></contrib></contrib-group><aff id="af1-phrp-08-373"><label>a</label>Department of Statistics, Chonnam National University, Gwangju, Korea</aff><aff id="af2-phrp-08-373"><label>b</label>Department of Mathematics, Kyungpook National University, Daegu, Korea</aff><author-notes><corresp id="c1-phrp-08-373">Corresponding author: Yongkuk Kim, E-mail: <email>yongkuk@knu.ac.kr</email></corresp></author-notes><pub-date pub-type="ppub"><month>12</month><year>2017</year></pub-date><pub-date pub-type="epub"><day>31</day><month>12</month><year>2017</year></pub-date><volume>8</volume><issue>6</issue><fpage>373</fpage><lpage>376</lpage><history><date date-type="received"><day>05</day><month>9</month><year>2017</year></date><date date-type="rev-recd"><day>02</day><month>11</month><year>2017</year></date><date date-type="accepted"><day>09</day><month>11</month><year>2017</year></date></history><permissions><copyright-statement>Copyright ©2017, Korea Centers for Disease Control and Prevention</copyright-statement><copyright-year>2017</copyright-year><license license-type="open-access" xlink:href="http://creativecommons.org/licenses/by-nc-nd/4.0/"><license-p><pmc-comment>CREATIVE COMMONS</pmc-comment>This is an open access article under the CC BY-NC-ND license (<ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/licenses/by-nc-nd/4.0/">http://creativecommons.org/licenses/by-nc-nd/4.0/</ext-link>).</license-p></license></permissions><abstract><sec><title>Objectives</title><p>The 2015 Middle East Respiratory Syndrome Coronavirus (MERS-CoV) outbreak in Korea caused major economic and social problems. The control intervention was conducted during the MERS-CoV outbreak in Korea immediately after the confirmation of the index case. This study investigates whether the early risk communication with the general public and mass media is an effective preventive strategy.</p></sec><sec><title>Methods</title><p>The SEIR (Susceptible, Exposed, Infectious, Recovered) model with estimated parameters for the time series data of the daily MERS-CoV incidence in Korea was considered from May to December 2015. For 10,000 stochastic simulations, the SEIR model was computed using the Gillespie algorithm. Depending on the time of control intervention on the 20th, 40th, and 60th days after the identification of the index case, the box plots of MERS-CoV incidences in Korea were computed, and the results were analyzed via ANOVA.</p></sec><sec><title>Results</title><p>The box plots showed that there was a significant difference between the non-intervention and intervention groups (the 20th day, 40th day, and 60th day groups) and seemed to show no significant difference based on the time of intervention. However, the ANOVA revealed that early intervention was a good strategy to control the disease.</p></sec><sec><title>Conclusion</title><p>Appropriate risk communication can secure the confidence of the general public in the public health authorities.</p></sec></abstract><kwd-group><kwd>infectious disease transmission</kwd><kwd>basic reproduction number</kwd><kwd>Middle East respiratory syndrome coronavirus</kwd></kwd-group></article-meta></front><body><sec sec-type="intro"><title>INTRODUCTION</title><p>The emergence of Middle East respiratory syndrome coronavirus (MERS-CoV) in South Korea in 2015 exerted huge social and economic tolls. Mathematical models are effective for understanding and controlling the spread of MERS-CoV, and so far, many attempts at applying mathematical models have been made to understand the MERS-CoV outbreak in Korea [<xref rid="b1-phrp-08-373" ref-type="bibr">1</xref>–<xref rid="b9-phrp-08-373" ref-type="bibr">9</xref>]. The control intervention was conducted during the MERS-CoV outbreak in Korea immediately after the confirmation of the index case. Using a mathematical model, we investigated whether the early risk communication with the general public and mass media is an effective preventive strategy.</p><p>The SEIR (Susceptible, Exposed, Infectious, Recovered) model with estimated parameters from the time series data on the daily incidence of MERS-CoV in Korea was considered from May to December 2015. For the 10,000 stochastic simulations, the SEIR model was computed using the Gillespie algorithm. Depending on the time of control interventions on the 20th, 40th, and 60th days since the index case was identified, the box plots of MERS-CoV incidences in Korea were computed, and then analysis of variance (ANOVA) was used to analyze the results.</p></sec><sec sec-type="materials|methods"><title>MATERIALS AND METHODS</title><sec><title>1. The basic model for MERS-CoV dynamics</title><p>The following SEIR model by Lee et al. [<xref rid="b10-phrp-08-373" ref-type="bibr">10</xref>] that categorizes each individual into one of the six epidemiological classes was considered: susceptible (S), exposed (or high-risk latent) (E), symptomatic and infectious (I), infectious but asymptomatic (A), hospitalized (H), and recovered (R).</p><disp-formula id="fd1-phrp-08-373"><mml:math id="m1"><mml:mrow><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mo>-</mml:mo><mml:mi>β</mml:mi><mml:mfrac><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>I</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mi>H</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>N</mml:mi></mml:mfrac><mml:mi> </mml:mi><mml:mi>S</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>E</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>β</mml:mi><mml:mfrac><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>I</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mi>A</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mi>H</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mi>N</mml:mi></mml:mfrac><mml:mi> </mml:mi><mml:mi>S</mml:mi><mml:mo>-</mml:mo><mml:mi>κ</mml:mi><mml:mi>E</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>I</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>κ</mml:mi><mml:mi>ρ</mml:mi><mml:mi>E</mml:mi><mml:mo>-</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mi>a</mml:mi></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mi>I</mml:mi></mml:msub><mml:mo stretchy="false">)</mml:mo><mml:mi>I</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>A</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mi>κ</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>1</mml:mn><mml:mo>-</mml:mo><mml:mi>ρ</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mi>E</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mi>I</mml:mi></mml:msub><mml:mi>A</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>H</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mi>a</mml:mi></mml:msub><mml:mi>I</mml:mi><mml:mo>-</mml:mo><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mi>r</mml:mi></mml:msub><mml:mi>H</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mi>I</mml:mi></mml:msub><mml:mi>I</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mi>r</mml:mi></mml:msub><mml:mi>H</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mi>I</mml:mi></mml:msub><mml:mi>A</mml:mi></mml:mtd></mml:mtr></mml:mtable></mml:mrow></mml:math></disp-formula><p>It was assumed that not only infectious and hospitalized individuals, but also asymptomatic individuals could infect others. The parameters β, <italic>l</italic><italic><sub>1</sub></italic>, <italic>l</italic><italic><sub>2</sub></italic>, <italic>κ</italic>, <italic>ρ</italic>, <italic>γ</italic><italic><sub>a</sub></italic>, <italic>γ</italic><italic><sub>I</sub></italic> and <italic>γ</italic><italic><sub>r</sub></italic> represent human-to-human transmission rate per unit time, the relative transmissibility of asymptomatic and hospitalized classes, the rate of progression from exposed class <italic>E</italic> to symptomatic <italic>I</italic> or asymptomatic infectious class <italic>A</italic>, the proportion of symptomatic infections, the hospitalization rate of symptomatic individuals, the recovery rate without being hospitalized, and the recovery rate of hospitalized patients, respectively.</p></sec><sec><title>2. Stochastic simulation methods</title><p>We used the Gillespie algorithm to study random interactions occurring in the given system of equations. The stochastic simulation algorithm, suggested by Gillespie [<xref rid="b11-phrp-08-373" ref-type="bibr">11</xref>], is as follows:</p><p>For a set of coupled ordinary differential equations</p><disp-formula id="fd2-phrp-08-373"><mml:math id="m2"><mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:mi>d</mml:mi><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>j</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>M</mml:mi></mml:munderover><mml:mrow><mml:msub><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mi>j</mml:mi></mml:msub><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mi>j</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>,</mml:mo></mml:mrow></mml:mrow></mml:math></disp-formula><p>we can construct an exact numerical realization of the process <italic>X</italic>(<italic>t</italic>):</p><list list-type="simple"><list-item><p>Step 0: Initialize the time <italic>t</italic> = <italic>t</italic><sub>0</sub> and the system’s state <italic>X</italic>(<italic>t</italic><sub>0</sub>) = <italic>X</italic><sub>0</sub>.</p></list-item><list-item><p>Step 1: With the system in state <italic>X</italic> at time <italic>t</italic>, evaluate all the <italic>a</italic><italic><sub>j</sub></italic>(<italic>X</italic>) and their sum <inline-formula><mml:math id="m3"><mml:mrow><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>:</mml:mo><mml:mo>=</mml:mo><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>M</mml:mi></mml:msubsup><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula>.</p></list-item><list-item><p>Step 2: Draw two random numbers <italic>r</italic><sub>1</sub> and <italic>r</italic><sub>2</sub> from the uniform distribution in the unit interval, and take</p><p><disp-formula id="fd3-phrp-08-373"><mml:math id="m4"><mml:mrow><mml:mrow><mml:mi mathvariant="normal">τ</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mfrac><mml:mi> </mml:mi><mml:mtext>ln</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mrow><mml:mi>r</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula></p><p>j=the smallest integer satisfying <inline-formula><mml:math id="m5"><mml:mrow><mml:mrow><mml:mstyle displaystyle="true"><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>j</mml:mi></mml:munderover></mml:mstyle><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mo>></mml:mo><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mo>:</mml:mo><mml:mo>=</mml:mo><mml:mstyle displaystyle="true"><mml:munderover><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>M</mml:mi></mml:munderover></mml:mstyle><mml:mrow><mml:msub><mml:mrow><mml:mi>a</mml:mi></mml:mrow><mml:mi>i</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>X</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></inline-formula></p></list-item><list-item><p>Step 3: Replace <italic>t</italic> ← <italic>t</italic> + τ and <italic>X</italic> ← <italic>X</italic> + <italic>c</italic><italic><sub>j</sub></italic>.</p></list-item><list-item><p>Step 4: Record (<italic>X</italic>, <italic>t</italic>) as desired. Return to Step 1, or else end the simulation.</p></list-item></list></sec></sec><sec sec-type="results"><title>RESULTS</title><p>For the 10,000 stochastic simulations, the SEIR model was computed by using the Gillespie algorithm with initial values <italic>S</italic> = <italic>100,000</italic>; <italic>E</italic> = <italic>10</italic>; <italic>I</italic> = <italic>A</italic> = <italic>H</italic> = <italic>R</italic> = <italic>0</italic> and the parameter values [<xref rid="b10-phrp-08-373" ref-type="bibr">10</xref>] β = 0.085, <italic>l</italic><sub>1</sub> = 0.2, <italic>l</italic><sub>2</sub> = 10, <italic>κ</italic> = 1/6.6, <italic>ρ</italic> = 0.585, <italic>γ</italic><italic><sub>a</sub></italic> = 0.6403, <italic>γ</italic><italic><sub>I</sub></italic> = 1/5, and <italic>γ</italic><italic><sub>r</sub></italic> = 1/7. The control measure was used by changing the value <italic>l</italic><sub>2</sub> from 10 to 8.5. <xref rid="f1-phrp-08-373" ref-type="fig">Figure 1</xref> depicts the box plots of incidences <italic>I</italic> (<italic>t</italic>) + <italic>A</italic> (<italic>t</italic>) + <italic>H</italic> (<italic>t</italic>) of the MERS-CoV depending on the time of the control intervention on the 20th, 40th, and 60th days after the identification of the index case.</p><p>The box plots showed that there was a significant difference between the non-intervention and intervention groups (the 20th day, 40th day, and 60th day groups) and seemed to show no significant difference based on the time of intervention. However, the ANOVA in <xref rid="t1-phrp-08-373" ref-type="table">Table 1</xref> revealed a significant difference between the averages in the intervention groups and showed that early intervention promotes a good strategy to control the disease. In particular, these results were evident from the average and standard deviation, which were smaller in the early intervention period. The difference was markedly larger 100 days after the identification of the index case, and the difference in the effect of the intervention over time showed a decreasing trend.</p></sec><sec sec-type="discussion"><title>DISCUSSION</title><p>The control intervention was conducted during the MERS-CoV outbreak in Korea immediately after the confirmation of the index case and the control measures were carried out on the 20th day after the confirmation of the index case. Using the stochastic simulations of the SEIR model depending on the time of control interventions on the 20th, 40th, and 60th days after the confirmation of the index case, this study investigated whether early risk communication with the general public and mass media is an effective preventive strategy. As a result, the intervention on the 20th day after the identification of the index case was much better than the intervention on the 60th day. Therefore, we conclude that appropriate risk communication can secure the confidence of the general public in the public health authorities.</p></sec></body><back><ack><title>ACKNOWLEDGMENTS</title><p>This study was carried out with the support of the Research Program of Rural Development Administration, Republic of Korea (Project No. PJ011563).</p></ack><fn-group><fn id="fn1-phrp-08-373" fn-type="COI-statement"><p><bold>CONFLICTS OF INTEREST</bold></p><p>No potential conflict of interest relevant to this article was reported.</p></fn></fn-group><ref-list><title>REFERENCES</title><ref id="b1-phrp-08-373"><label>1</label><element-citation publication-type="journal"><person-group person-group-type="author"><name><surname>Hsieh</surname><given-names>YH</given-names></name></person-group><article-title>2015 Middle East respiratory syndrome coronavirus (MERS-CoV) nosocomial outbreak in South Korea: insights from modeling</article-title><source>PeerJ</source><year>2015</year><volume>3</volume><fpage>e1505</fpage><comment><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.7717/peerj.1505">https://doi.org/10.7717/peerj.1505</ext-link></comment><pub-id pub-id-type="doi">10.7717/peerj.1505</pub-id><pmc-comment>4690341 </pmc-comment>
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Chem</source><year>1977</year><volume>81</volume><fpage>2340</fpage><lpage>61</lpage><comment><ext-link ext-link-type="uri" xlink:href="https://doi.org/10.1021/j100540a008">https://doi.org/10.1021/j100540a008</ext-link></comment><pub-id pub-id-type="doi">10.1021/j100540a008</pub-id></element-citation></ref></ref-list></back><floats-group><fig id="f1-phrp-08-373" orientation="portrait" position="float"><label>Figure 1</label><caption><p>Box plot for the control interventions according to the number of days (A, 100 days; B, 200 days; C, 300 days; D, 400 days) after the identification of the index case.</p></caption><graphic xlink:href="phrp-08-373f1"></graphic></fig><table-wrap id="t1-phrp-08-373" orientation="portrait" position="float"><label>Table 1</label><caption><p>Results of the ANOVA according to the day of intervention after the identification of the index case</p></caption><table frame="hsides" rules="groups"><thead><tr><th valign="bottom" align="center" rowspan="1" colspan="1">Variable</th><th valign="bottom" align="center" rowspan="1" colspan="1">Data</th><th valign="bottom" align="center" rowspan="1" colspan="1">ANOVA (F-value)<xref rid="tfn2-phrp-08-373" ref-type="table-fn">a</xref></th></tr></thead><tbody><tr><td valign="top" align="left" rowspan="1" colspan="1">The 100th day</td><td valign="top" align="center" rowspan="1" colspan="1"></td><td valign="top" align="center" rowspan="1" colspan="1">231.72</td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> No control</td><td valign="top" align="center" rowspan="1" colspan="1">23.0017 ± 30.1585</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 20th day control</td><td valign="top" align="center" rowspan="1" colspan="1">9.4533 ± 14.3353</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 40th day control</td><td valign="top" align="center" rowspan="1" colspan="1">11.4083 ± 16.0851</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 60th day control</td><td valign="top" align="center" rowspan="1" colspan="1">14.5683 ± 19.9566</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1">The 200th day</td><td valign="top" align="center" rowspan="1" colspan="1"></td><td valign="top" align="center" rowspan="1" colspan="1">108.49</td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> No control</td><td valign="top" align="center" rowspan="1" colspan="1">52.6752 ± 82.3164</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 20th day control</td><td valign="top" align="center" rowspan="1" colspan="1">7.3237 ± 16.8129</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 40th day control</td><td valign="top" align="center" rowspan="1" colspan="1">8.6575 ± 18.1072</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 60th day control</td><td valign="top" align="center" rowspan="1" colspan="1">11.2189 ± 21.7501</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1">The 300th day</td><td valign="top" align="center" rowspan="1" colspan="1"></td><td valign="top" align="center" rowspan="1" colspan="1">66.99</td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> No control</td><td valign="top" align="center" rowspan="1" colspan="1">106.4571 ± 164.5254</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 20th day control</td><td valign="top" align="center" rowspan="1" colspan="1">5.5167 ± 16.7547</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 40th day control</td><td valign="top" align="center" rowspan="1" colspan="1">6.3517 ± 17.2051</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 60th day control</td><td valign="top" align="center" rowspan="1" colspan="1">8.4170 ± 20.5291</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1">The 400th day</td><td valign="top" align="center" rowspan="1" colspan="1"></td><td valign="top" align="center" rowspan="1" colspan="1">38.18</td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> No control</td><td valign="top" align="center" rowspan="1" colspan="1">172.5906 ± 241.5982</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 20th day control</td><td valign="top" align="center" rowspan="1" colspan="1">3.9101 ± 14.7193</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 40th day control</td><td valign="top" align="center" rowspan="1" colspan="1">4.4760 ± 15.3066</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr><tr><td colspan="3" valign="bottom" align="left" rowspan="1"><hr></hr></td></tr><tr><td valign="top" align="left" rowspan="1" colspan="1"> The 60th day control</td><td valign="top" align="center" rowspan="1" colspan="1">5.8240 ± 17.5711</td><td valign="top" align="center" rowspan="1" colspan="1"></td></tr></tbody></table><table-wrap-foot><fn id="tfn1-phrp-08-373"><p>Value are presented as mean ± standard deviation.</p></fn><fn id="tfn2-phrp-08-373"><label>a</label><p>Degree of freedom (d.f.) 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