The daily computed weighted averaging basic reproduction number R0,k,ωn for MERS-CoV in South Korea
Identifieur interne : 000982 ( Pmc/Checkpoint ); précédent : 000981; suivant : 000983The daily computed weighted averaging basic reproduction number R0,k,ωn for MERS-CoV in South Korea
Auteurs : Darae Jeong [Corée du Sud] ; Chang Hyeong Lee [Corée du Sud] ; Yongho Choi [Corée du Sud] ; Junseok Kim [Corée du Sud]Source :
- Physica a [ 0378-4371 ] ; 2016.
Abstract
In this paper, we propose the daily computed weighted averaging basic reproduction number
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DOI: 10.1016/j.physa.2016.01.072
PubMed: 32288098
PubMed Central: 7126530
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">The daily computed weighted averaging basic reproduction number <inline-formula><mml:math id="M1" altimg="si7.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> for MERS-CoV in South Korea</title><author><name sortKey="Jeong, Darae" sort="Jeong, Darae" uniqKey="Jeong D" first="Darae" last="Jeong">Darae Jeong</name><affiliation wicri:level="1"><nlm:aff id="af000005">Department of Mathematics, Korea University, Seoul 136-713, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Mathematics, Korea University, Seoul 136-713</wicri:regionArea><placeName><settlement type="city">Séoul</settlement><region type="capital">Région capitale de Séoul</region></placeName></affiliation></author><author><name sortKey="Lee, Chang Hyeong" sort="Lee, Chang Hyeong" uniqKey="Lee C" first="Chang Hyeong" last="Lee">Chang Hyeong Lee</name><affiliation wicri:level="1"><nlm:aff id="af000010">Department of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798</wicri:regionArea><wicri:noRegion>Ulsan 689-798</wicri:noRegion></affiliation></author><author><name sortKey="Choi, Yongho" sort="Choi, Yongho" uniqKey="Choi Y" first="Yongho" last="Choi">Yongho Choi</name><affiliation wicri:level="1"><nlm:aff id="af000005">Department of Mathematics, Korea University, Seoul 136-713, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Mathematics, Korea University, Seoul 136-713</wicri:regionArea><placeName><settlement type="city">Séoul</settlement><region type="capital">Région capitale de Séoul</region></placeName></affiliation></author><author><name sortKey="Kim, Junseok" sort="Kim, Junseok" uniqKey="Kim J" first="Junseok" last="Kim">Junseok Kim</name><affiliation wicri:level="1"><nlm:aff id="af000005">Department of Mathematics, Korea University, Seoul 136-713, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Mathematics, Korea University, Seoul 136-713</wicri:regionArea><placeName><settlement type="city">Séoul</settlement><region type="capital">Région capitale de Séoul</region></placeName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">32288098</idno><idno type="pmc">7126530</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7126530</idno><idno type="RBID">PMC:7126530</idno><idno type="doi">10.1016/j.physa.2016.01.072</idno><date when="2016">2016</date><idno type="wicri:Area/Pmc/Corpus">001123</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">001123</idno><idno type="wicri:Area/Pmc/Curation">001123</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Curation">001123</idno><idno type="wicri:Area/Pmc/Checkpoint">000982</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Checkpoint">000982</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">The daily computed weighted averaging basic reproduction number <inline-formula><mml:math id="M1" altimg="si7.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> for MERS-CoV in South Korea</title><author><name sortKey="Jeong, Darae" sort="Jeong, Darae" uniqKey="Jeong D" first="Darae" last="Jeong">Darae Jeong</name><affiliation wicri:level="1"><nlm:aff id="af000005">Department of Mathematics, Korea University, Seoul 136-713, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Mathematics, Korea University, Seoul 136-713</wicri:regionArea><placeName><settlement type="city">Séoul</settlement><region type="capital">Région capitale de Séoul</region></placeName></affiliation></author><author><name sortKey="Lee, Chang Hyeong" sort="Lee, Chang Hyeong" uniqKey="Lee C" first="Chang Hyeong" last="Lee">Chang Hyeong Lee</name><affiliation wicri:level="1"><nlm:aff id="af000010">Department of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798</wicri:regionArea><wicri:noRegion>Ulsan 689-798</wicri:noRegion></affiliation></author><author><name sortKey="Choi, Yongho" sort="Choi, Yongho" uniqKey="Choi Y" first="Yongho" last="Choi">Yongho Choi</name><affiliation wicri:level="1"><nlm:aff id="af000005">Department of Mathematics, Korea University, Seoul 136-713, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Mathematics, Korea University, Seoul 136-713</wicri:regionArea><placeName><settlement type="city">Séoul</settlement><region type="capital">Région capitale de Séoul</region></placeName></affiliation></author><author><name sortKey="Kim, Junseok" sort="Kim, Junseok" uniqKey="Kim J" first="Junseok" last="Kim">Junseok Kim</name><affiliation wicri:level="1"><nlm:aff id="af000005">Department of Mathematics, Korea University, Seoul 136-713, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Mathematics, Korea University, Seoul 136-713</wicri:regionArea><placeName><settlement type="city">Séoul</settlement><region type="capital">Région capitale de Séoul</region></placeName></affiliation></author></analytic><series><title level="j">Physica a</title><idno type="ISSN">0378-4371</idno><idno type="eISSN">0378-4371</idno><imprint><date when="2016">2016</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><p>In this paper, we propose the daily computed weighted averaging basic reproduction number <inline-formula><mml:math id="M2" altimg="si7.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> for Middle East respiratory syndrome coronavirus (MERS-CoV) outbreak in South Korea, May to July 2015. We use an SIR model with piecewise constant parameters <inline-formula><mml:math id="M3" altimg="si31.gif" display="inline" overflow="scroll"><mml:mi>β</mml:mi></mml:math></inline-formula> (contact rate) and <inline-formula><mml:math id="M4" altimg="si32.gif" display="inline" overflow="scroll"><mml:mi>γ</mml:mi></mml:math></inline-formula> (removed rate). We use the explicit Euler’s method for the solution of the SIR model and a nonlinear least-square fitting procedure for finding the best parameters. In <inline-formula><mml:math id="M5" altimg="si7.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula>, the parameters <inline-formula><mml:math id="M6" altimg="si23.gif" display="inline" overflow="scroll"><mml:mi>n</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M7" altimg="si35.gif" display="inline" overflow="scroll"><mml:mi>k</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M8" altimg="si36.gif" display="inline" overflow="scroll"><mml:mi>w</mml:mi></mml:math></inline-formula> denote days from a reference date, the number of days in averaging, and a weighting factor, respectively. We perform a series of numerical experiments and compare the results with the real-world data. In particular, using the predicted reproduction number based on the previous two consecutive reproduction numbers, we can predict the future behavior of the reproduction number.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Zhang, X" uniqKey="Zhang X">X. Zhang</name></author><author><name sortKey="Ge, B" uniqKey="Ge B">B. Ge</name></author><author><name sortKey="Wang, Q" uniqKey="Wang Q">Q. Wang</name></author><author><name sortKey="Jiang, J" uniqKey="Jiang J">J. Jiang</name></author><author><name sortKey="You, H" uniqKey="You H">H. You</name></author><author><name sortKey="Chen, Y" uniqKey="Chen Y">Y. Chen</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Cowling, B J" uniqKey="Cowling B">B.J. Cowling</name></author><author><name sortKey="Park, M" uniqKey="Park M">M. Park</name></author><author><name sortKey="Fang, V J" uniqKey="Fang V">V.J. 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Physica A</journal-id><journal-id journal-id-type="iso-abbrev">Physica A</journal-id><journal-title-group><journal-title>Physica a</journal-title></journal-title-group><issn pub-type="ppub">0378-4371</issn><issn pub-type="epub">0378-4371</issn><publisher><publisher-name>Elsevier B.V.</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">32288098</article-id><article-id pub-id-type="pmc">7126530</article-id><article-id pub-id-type="publisher-id">S0378-4371(16)00126-6</article-id><article-id pub-id-type="doi">10.1016/j.physa.2016.01.072</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>The daily computed weighted averaging basic reproduction number <inline-formula><mml:math id="M1" altimg="si7.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> for MERS-CoV in South Korea</article-title></title-group><contrib-group><contrib contrib-type="author" id="au000005"><name><surname>Jeong</surname><given-names>Darae</given-names></name><xref rid="af000005" ref-type="aff">a</xref></contrib><contrib contrib-type="author" id="au000010"><name><surname>Lee</surname><given-names>Chang Hyeong</given-names></name><xref rid="af000010" ref-type="aff">b</xref></contrib><contrib contrib-type="author" id="au000015"><name><surname>Choi</surname><given-names>Yongho</given-names></name><xref rid="af000005" ref-type="aff">a</xref></contrib><contrib contrib-type="author" id="au000020"><name><surname>Kim</surname><given-names>Junseok</given-names></name><email>cfdkim@korea.ac.kr</email><email>http://math.korea.ac.kr/~cfdkim/</email><xref rid="af000005" ref-type="aff">a</xref><xref rid="cor000005" ref-type="corresp">⁎</xref></contrib></contrib-group><aff id="af000005"><label>a</label>Department of Mathematics, Korea University, Seoul 136-713, Republic of Korea</aff><aff id="af000010"><label>b</label>Department of Mathematical Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, Republic of Korea</aff><author-notes><corresp id="cor000005"><label>⁎</label>Corresponding author. <email>cfdkim@korea.ac.kr</email><email>http://math.korea.ac.kr/~cfdkim/</email></corresp></author-notes><pub-date pub-type="pmc-release"><day>2</day><month>2</month><year>2016</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"><day>1</day><month>6</month><year>2016</year></pub-date><pub-date pub-type="epub"><day>2</day><month>2</month><year>2016</year></pub-date><volume>451</volume><fpage>190</fpage><lpage>197</lpage><history><date date-type="received"><day>8</day><month>12</month><year>2015</year></date><date date-type="rev-recd"><day>8</day><month>1</month><year>2016</year></date></history><permissions><copyright-statement>Copyright © 2016 Elsevier B.V. All rights reserved.</copyright-statement><copyright-year>2016</copyright-year><copyright-holder>Elsevier B.V.</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="a000005"><p>In this paper, we propose the daily computed weighted averaging basic reproduction number <inline-formula><mml:math id="M2" altimg="si7.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula> for Middle East respiratory syndrome coronavirus (MERS-CoV) outbreak in South Korea, May to July 2015. We use an SIR model with piecewise constant parameters <inline-formula><mml:math id="M3" altimg="si31.gif" display="inline" overflow="scroll"><mml:mi>β</mml:mi></mml:math></inline-formula> (contact rate) and <inline-formula><mml:math id="M4" altimg="si32.gif" display="inline" overflow="scroll"><mml:mi>γ</mml:mi></mml:math></inline-formula> (removed rate). We use the explicit Euler’s method for the solution of the SIR model and a nonlinear least-square fitting procedure for finding the best parameters. In <inline-formula><mml:math id="M5" altimg="si7.gif" display="inline" overflow="scroll"><mml:msubsup><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>ω</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msubsup></mml:math></inline-formula>, the parameters <inline-formula><mml:math id="M6" altimg="si23.gif" display="inline" overflow="scroll"><mml:mi>n</mml:mi></mml:math></inline-formula>, <inline-formula><mml:math id="M7" altimg="si35.gif" display="inline" overflow="scroll"><mml:mi>k</mml:mi></mml:math></inline-formula>, and <inline-formula><mml:math id="M8" altimg="si36.gif" display="inline" overflow="scroll"><mml:mi>w</mml:mi></mml:math></inline-formula> denote days from a reference date, the number of days in averaging, and a weighting factor, respectively. We perform a series of numerical experiments and compare the results with the real-world data. In particular, using the predicted reproduction number based on the previous two consecutive reproduction numbers, we can predict the future behavior of the reproduction number.</p></abstract><abstract abstract-type="author-highlights" id="a000010"><title>Highlights</title><p><list list-type="simple" id="l000005"><list-item id="li000005"><label>•</label><p id="p000005">We propose the daily basic reproduction number for MERS-CoV in South Korea.</p></list-item><list-item id="li000010"><label>•</label><p id="p000010">We use an SIR model with piecewise constant contact and removed rates.</p></list-item><list-item id="li000015"><label>•</label><p id="p000015">We apply the explicit Euler’s method for the solution of the SIR model.</p></list-item><list-item id="li000020"><label>•</label><p id="p000020">We use nonlinear least-square fitting procedure for finding the best parameters.</p></list-item></list></p></abstract><kwd-group id="ks000005"><title>Keywords</title><kwd>MERS-CoV</kwd><kwd>SIR model</kwd><kwd>Explicit Euler’s method</kwd><kwd>Optimal parameter fitting</kwd></kwd-group></article-meta></front></pmc><affiliations><list><country><li>Corée du Sud</li></country><region><li>Région capitale de Séoul</li></region><settlement><li>Séoul</li></settlement></list><tree><country name="Corée du Sud"><region name="Région capitale de Séoul"><name sortKey="Jeong, Darae" sort="Jeong, Darae" uniqKey="Jeong D" first="Darae" last="Jeong">Darae Jeong</name></region><name sortKey="Choi, Yongho" sort="Choi, Yongho" uniqKey="Choi Y" first="Yongho" last="Choi">Yongho Choi</name><name sortKey="Kim, Junseok" sort="Kim, Junseok" uniqKey="Kim J" first="Junseok" last="Kim">Junseok Kim</name><name sortKey="Lee, Chang Hyeong" sort="Lee, Chang Hyeong" uniqKey="Lee C" first="Chang Hyeong" last="Lee">Chang Hyeong Lee</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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