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
Url:
DOI: 10.1016/j.physa.2016.01.072
PubMed: 32288098
PubMed Central: 7126530
Affiliations:
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<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>
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<mml:mo>,</mml:mo>
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<mml:mrow><mml:mi>n</mml:mi>
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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>
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<author><name sortKey="Lee, Chang Hyeong" sort="Lee, Chang Hyeong" uniqKey="Lee C" first="Chang Hyeong" last="Lee">Chang Hyeong Lee</name>
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<author><name sortKey="Choi, Yongho" sort="Choi, Yongho" uniqKey="Choi Y" first="Yongho" last="Choi">Yongho Choi</name>
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<author><name sortKey="Kim, Junseok" sort="Kim, Junseok" uniqKey="Kim J" first="Junseok" last="Kim">Junseok Kim</name>
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<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>
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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>
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<issn pub-type="epub">0378-4371</issn>
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<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>
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<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>
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<mml:mrow><mml:mi>n</mml:mi>
</mml:mrow>
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</mml:math>
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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>
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<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>
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<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>
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