Investigation of nonlinear epidemiological models for analyzing and controlling the MERS outbreak in Korea
Identifieur interne : 000815 ( Pmc/Checkpoint ); précédent : 000814; suivant : 000816Investigation of nonlinear epidemiological models for analyzing and controlling the MERS outbreak in Korea
Auteurs : Inkyung Ahn [Corée du Sud] ; Seongman Heo [Corée du Sud] ; Seunghyun Ji [Corée du Sud] ; Kyung Hyun Kim [Corée du Sud] ; Taehwan Kim [Corée du Sud] ; Eun Joo Lee [Corée du Sud] ; Jooyoung Park [Corée du Sud] ; Keehoon Sung [Corée du Sud]Source :
- Journal of Theoretical Biology [ 0022-5193 ] ; 2017.
Abstract
By fitting the SIQ model, which employs a squashing-type function for As a practical guideline to avoid another similar unexpected outbreak, we draw the conclusion that combined efforts in the early stage are critically important, and sharing information including the names of affected hospitals or countries, clinical situations, and prevention methods might be important for global public health control. We applied optimal control theory to the controlled SIQ model with the goal of minimizing the infectious compartment population and the cost of implementing the quarantine and isolation strategies. Simulation results show that the number of the MERS cases can be controlled reasonably well via the optimal control approach.
Url:
DOI: 10.1016/j.jtbi.2017.10.004
PubMed: 29031518
PubMed Central: 7094113
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<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Investigation of nonlinear epidemiological models for analyzing and controlling the MERS outbreak in Korea</title><author><name sortKey="Ahn, Inkyung" sort="Ahn, Inkyung" uniqKey="Ahn I" first="Inkyung" last="Ahn">Inkyung Ahn</name><affiliation wicri:level="1"><nlm:aff id="aff0001">Department of Mathematics, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Mathematics, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Heo, Seongman" sort="Heo, Seongman" uniqKey="Heo S" first="Seongman" last="Heo">Seongman Heo</name><affiliation wicri:level="1"><nlm:aff id="aff0002">Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Ji, Seunghyun" sort="Ji, Seunghyun" uniqKey="Ji S" first="Seunghyun" last="Ji">Seunghyun Ji</name><affiliation wicri:level="1"><nlm:aff id="aff0002">Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Kim, Kyung Hyun" sort="Kim, Kyung Hyun" uniqKey="Kim K" first="Kyung Hyun" last="Kim">Kyung Hyun Kim</name><affiliation wicri:level="1"><nlm:aff id="aff0003">Department of Biotechnology and Bioinformatics, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Biotechnology and Bioinformatics, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Kim, Taehwan" sort="Kim, Taehwan" uniqKey="Kim T" first="Taehwan" last="Kim">Taehwan Kim</name><affiliation wicri:level="1"><nlm:aff id="aff0002">Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Lee, Eun Joo" sort="Lee, Eun Joo" uniqKey="Lee E" first="Eun Joo" last="Lee">Eun Joo Lee</name><affiliation wicri:level="1"><nlm:aff id="aff0004">Department of Internal Medicine, Korea University Anam Hospital, College of Medicine, Korea University, Seoul, 136-705, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Internal Medicine, Korea University Anam Hospital, College of Medicine, Korea University, Seoul, 136-705</wicri:regionArea><wicri:noRegion>136-705</wicri:noRegion></affiliation></author><author><name sortKey="Park, Jooyoung" sort="Park, Jooyoung" uniqKey="Park J" first="Jooyoung" last="Park">Jooyoung Park</name><affiliation wicri:level="1"><nlm:aff id="aff0002">Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Sung, Keehoon" sort="Sung, Keehoon" uniqKey="Sung K" first="Keehoon" last="Sung">Keehoon Sung</name><affiliation wicri:level="1"><nlm:aff id="aff0002">Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">PMC</idno><idno type="pmid">29031518</idno><idno type="pmc">7094113</idno><idno type="url">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7094113</idno><idno type="RBID">PMC:7094113</idno><idno type="doi">10.1016/j.jtbi.2017.10.004</idno><date when="2017">2017</date><idno type="wicri:Area/Pmc/Corpus">000E85</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Corpus" wicri:corpus="PMC">000E85</idno><idno type="wicri:Area/Pmc/Curation">000E85</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Curation">000E85</idno><idno type="wicri:Area/Pmc/Checkpoint">000815</idno><idno type="wicri:explorRef" wicri:stream="Pmc" wicri:step="Checkpoint">000815</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a" type="main">Investigation of nonlinear epidemiological models for analyzing and controlling the MERS outbreak in Korea</title><author><name sortKey="Ahn, Inkyung" sort="Ahn, Inkyung" uniqKey="Ahn I" first="Inkyung" last="Ahn">Inkyung Ahn</name><affiliation wicri:level="1"><nlm:aff id="aff0001">Department of Mathematics, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Mathematics, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Heo, Seongman" sort="Heo, Seongman" uniqKey="Heo S" first="Seongman" last="Heo">Seongman Heo</name><affiliation wicri:level="1"><nlm:aff id="aff0002">Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Ji, Seunghyun" sort="Ji, Seunghyun" uniqKey="Ji S" first="Seunghyun" last="Ji">Seunghyun Ji</name><affiliation wicri:level="1"><nlm:aff id="aff0002">Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Kim, Kyung Hyun" sort="Kim, Kyung Hyun" uniqKey="Kim K" first="Kyung Hyun" last="Kim">Kyung Hyun Kim</name><affiliation wicri:level="1"><nlm:aff id="aff0003">Department of Biotechnology and Bioinformatics, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Biotechnology and Bioinformatics, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Kim, Taehwan" sort="Kim, Taehwan" uniqKey="Kim T" first="Taehwan" last="Kim">Taehwan Kim</name><affiliation wicri:level="1"><nlm:aff id="aff0002">Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Lee, Eun Joo" sort="Lee, Eun Joo" uniqKey="Lee E" first="Eun Joo" last="Lee">Eun Joo Lee</name><affiliation wicri:level="1"><nlm:aff id="aff0004">Department of Internal Medicine, Korea University Anam Hospital, College of Medicine, Korea University, Seoul, 136-705, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Internal Medicine, Korea University Anam Hospital, College of Medicine, Korea University, Seoul, 136-705</wicri:regionArea><wicri:noRegion>136-705</wicri:noRegion></affiliation></author><author><name sortKey="Park, Jooyoung" sort="Park, Jooyoung" uniqKey="Park J" first="Jooyoung" last="Park">Jooyoung Park</name><affiliation wicri:level="1"><nlm:aff id="aff0002">Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author><author><name sortKey="Sung, Keehoon" sort="Sung, Keehoon" uniqKey="Sung K" first="Keehoon" last="Sung">Keehoon Sung</name><affiliation wicri:level="1"><nlm:aff id="aff0002">Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</nlm:aff><country xml:lang="fr">Corée du Sud</country><wicri:regionArea>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700</wicri:regionArea><wicri:noRegion>339-700</wicri:noRegion></affiliation></author></analytic><series><title level="j">Journal of Theoretical Biology</title><idno type="ISSN">0022-5193</idno><idno type="eISSN">1095-8541</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>Highlights</title><p><list list-type="simple" id="celist0001"><list-item id="celistitem0001"><label>•</label><p id="para0001">By fitting the SIQ model, which employs a squashing-type function for <italic>β</italic>(t), to the real data on the confirmed cases and the quarantined cases, we obtained reasonable performance. Also, it turned out that the resultant estimated parameters belonged to plausible ranges. By comparison, the conventional SIQ model utilizing a constant transmission probability could not explain the observed data well.</p></list-item><list-item id="celistitem0002"><label>•</label><p id="para0002">As a practical guideline to avoid another similar unexpected outbreak, we draw the conclusion that combined efforts in the early stage are critically important, and sharing information including the names of affected hospitals or countries, clinical situations, and prevention methods might be important for global public health control.</p></list-item><list-item id="celistitem0003"><label>•</label><p id="para0003">We applied optimal control theory to the controlled SIQ model with the goal of minimizing the infectious compartment population and the cost of implementing the quarantine and isolation strategies. Simulation results show that the number of the MERS cases can be controlled reasonably well via the optimal control approach.</p></list-item></list></p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Bishop, C M" uniqKey="Bishop C">C.M. Bishop</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Buonomo, B" uniqKey="Buonomo B">B. Buonomo</name></author><author><name sortKey="Messina, E" uniqKey="Messina E">E. Messina</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Caetano, M A L" uniqKey="Caetano M">M.A.L. Caetano</name></author><author><name sortKey="Yoneyama, T" uniqKey="Yoneyama T">T. Yoneyama</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Castillo Chavez, C" uniqKey="Castillo Chavez C">C. Castillo-Chavez</name></author><author><name sortKey="Castillo Garsow, C W" uniqKey="Castillo Garsow C">C.W. 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<front><journal-meta><journal-id journal-id-type="nlm-ta">J Theor Biol</journal-id><journal-id journal-id-type="iso-abbrev">J. Theor. Biol</journal-id><journal-title-group><journal-title>Journal of Theoretical Biology</journal-title></journal-title-group><issn pub-type="ppub">0022-5193</issn><issn pub-type="epub">1095-8541</issn><publisher><publisher-name>Elsevier Ltd.</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">29031518</article-id><article-id pub-id-type="pmc">7094113</article-id><article-id pub-id-type="publisher-id">S0022-5193(17)30466-6</article-id><article-id pub-id-type="doi">10.1016/j.jtbi.2017.10.004</article-id><article-categories><subj-group subj-group-type="heading"><subject>Article</subject></subj-group></article-categories><title-group><article-title>Investigation of nonlinear epidemiological models for analyzing and controlling the MERS outbreak in Korea</article-title></title-group><contrib-group><contrib contrib-type="author" id="au0001"><name><surname>Ahn</surname><given-names>Inkyung</given-names></name><email>ahnik@korea.ac.kr</email><xref rid="cor0001" ref-type="corresp">⁎</xref><xref rid="aff0001" ref-type="aff">a</xref></contrib><contrib contrib-type="author" id="au0002"><name><surname>Heo</surname><given-names>Seongman</given-names></name><xref rid="aff0002" ref-type="aff">b</xref></contrib><contrib contrib-type="author" id="au0003"><name><surname>Ji</surname><given-names>Seunghyun</given-names></name><xref rid="aff0002" ref-type="aff">b</xref></contrib><contrib contrib-type="author" id="au0004"><name><surname>Kim</surname><given-names>Kyung Hyun</given-names></name><xref rid="aff0003" ref-type="aff">c</xref></contrib><contrib contrib-type="author" id="au0005"><name><surname>Kim</surname><given-names>Taehwan</given-names></name><xref rid="aff0002" ref-type="aff">b</xref></contrib><contrib contrib-type="author" id="au0006"><name><surname>Lee</surname><given-names>Eun Joo</given-names></name><xref rid="aff0004" ref-type="aff">d</xref></contrib><contrib contrib-type="author" id="au0007"><name><surname>Park</surname><given-names>Jooyoung</given-names></name><email>parkj@korea.ac.kr</email><xref rid="cor0001" ref-type="corresp">⁎</xref><xref rid="aff0002" ref-type="aff">b</xref></contrib><contrib contrib-type="author" id="au0008"><name><surname>Sung</surname><given-names>Keehoon</given-names></name><xref rid="aff0002" ref-type="aff">b</xref></contrib></contrib-group><aff id="aff0001"><label>a</label>Department of Mathematics, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</aff><aff id="aff0002"><label>b</label>Department of Control and Instrumentation Engineering, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</aff><aff id="aff0003"><label>c</label>Department of Biotechnology and Bioinformatics, College of Science and Technology, Korea University, Sejong, 339-700, Republic of Korea</aff><aff id="aff0004"><label>d</label>Department of Internal Medicine, Korea University Anam Hospital, College of Medicine, Korea University, Seoul, 136-705, Republic of Korea</aff><author-notes><corresp id="cor0001"><label>⁎</label>Corresponding authors. <email>ahnik@korea.ac.kr</email><email>parkj@korea.ac.kr</email></corresp></author-notes><pub-date pub-type="pmc-release"><day>12</day><month>10</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"><day>21</day><month>1</month><year>2018</year></pub-date><pub-date pub-type="epub"><day>12</day><month>10</month><year>2017</year></pub-date><volume>437</volume><fpage>17</fpage><lpage>28</lpage><history><date date-type="received"><day>8</day><month>8</month><year>2016</year></date><date date-type="rev-recd"><day>18</day><month>9</month><year>2017</year></date><date date-type="accepted"><day>5</day><month>10</month><year>2017</year></date></history><permissions><copyright-statement>© 2017 Elsevier Ltd. All rights reserved.</copyright-statement><copyright-year>2017</copyright-year><copyright-holder>Elsevier Ltd</copyright-holder><license><license-p>Since January 2020 Elsevier has created a COVID-19 resource centre with free information in English and Mandarin on the novel coronavirus COVID-19. The COVID-19 resource centre is hosted on Elsevier Connect, the company's public news and information website. Elsevier hereby grants permission to make all its COVID-19-related research that is available on the COVID-19 resource centre - including this research content - immediately available in PubMed Central and other publicly funded repositories, such as the WHO COVID database with rights for unrestricted research re-use and analyses in any form or by any means with acknowledgement of the original source. These permissions are granted for free by Elsevier for as long as the COVID-19 resource centre remains active.</license-p></license></permissions><abstract abstract-type="author-highlights" id="absh001"><title>Highlights</title><p><list list-type="simple" id="celist0001"><list-item id="celistitem0001"><label>•</label><p id="para0001">By fitting the SIQ model, which employs a squashing-type function for <italic>β</italic>(t), to the real data on the confirmed cases and the quarantined cases, we obtained reasonable performance. Also, it turned out that the resultant estimated parameters belonged to plausible ranges. By comparison, the conventional SIQ model utilizing a constant transmission probability could not explain the observed data well.</p></list-item><list-item id="celistitem0002"><label>•</label><p id="para0002">As a practical guideline to avoid another similar unexpected outbreak, we draw the conclusion that combined efforts in the early stage are critically important, and sharing information including the names of affected hospitals or countries, clinical situations, and prevention methods might be important for global public health control.</p></list-item><list-item id="celistitem0003"><label>•</label><p id="para0003">We applied optimal control theory to the controlled SIQ model with the goal of minimizing the infectious compartment population and the cost of implementing the quarantine and isolation strategies. Simulation results show that the number of the MERS cases can be controlled reasonably well via the optimal control approach.</p></list-item></list></p></abstract><abstract id="abs0001"><p>Much concern has arisen regarding serious epidemics due to the Middle East Respiratory Syndrome (MERS) coronavirus. The first MERS case of Korea was reported on 20 May 2015, and since then, the MERS outbreak in Korea has resulted in hundreds of confirmed cases and tens of deaths. Deadly infectious diseases such as MERS have significant direct and indirect social impacts, which include disease-induced mortality and economic losses. Also, a delayed response to the outbreak and underestimating its danger can further aggravate the situation. Hence, an analysis and establishing efficient strategies for preventing the propagation of MERS is a very important and urgent issue. In this paper, we propose a class of nonlinear susceptible-infectious-quarantined (SIQ) models for analyzing and controlling the MERS outbreak in Korea. For the SIQ based ordinary differential equation (ODE) model, we perform the task of parameter estimation, and apply optimal control theory to the controlled SIQ model, with the goal of minimizing the infectious compartment population and the cost of implementing the quarantine and isolation strategies. Simulation results show that the proposed SIQ model can explain the observed data for the confirmed cases and the quarantined cases in the MERS outbreak very well, and the number of the MERS cases can be controlled reasonably well via the optimal control approach.</p></abstract><kwd-group id="keys0001"><title>Keywords</title><kwd>Optimal control</kwd><kwd>Epidemiological model</kwd><kwd>Parameter estimation</kwd><kwd>Coronavirus</kwd></kwd-group></article-meta></front></pmc><affiliations><list><country><li>Corée du Sud</li></country></list><tree><country name="Corée du Sud"><noRegion><name sortKey="Ahn, Inkyung" sort="Ahn, Inkyung" uniqKey="Ahn I" first="Inkyung" last="Ahn">Inkyung Ahn</name></noRegion><name sortKey="Heo, Seongman" sort="Heo, Seongman" uniqKey="Heo S" first="Seongman" last="Heo">Seongman Heo</name><name sortKey="Ji, Seunghyun" sort="Ji, Seunghyun" uniqKey="Ji S" first="Seunghyun" last="Ji">Seunghyun Ji</name><name sortKey="Kim, Kyung Hyun" sort="Kim, Kyung Hyun" uniqKey="Kim K" first="Kyung Hyun" last="Kim">Kyung Hyun Kim</name><name sortKey="Kim, Taehwan" sort="Kim, Taehwan" uniqKey="Kim T" first="Taehwan" last="Kim">Taehwan Kim</name><name sortKey="Lee, Eun Joo" sort="Lee, Eun Joo" uniqKey="Lee E" first="Eun Joo" last="Lee">Eun Joo Lee</name><name sortKey="Park, Jooyoung" sort="Park, Jooyoung" uniqKey="Park J" first="Jooyoung" last="Park">Jooyoung Park</name><name sortKey="Sung, Keehoon" sort="Sung, Keehoon" uniqKey="Sung K" first="Keehoon" last="Sung">Keehoon Sung</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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