Impact of Travel Between Patches for Spatial Spread of Disease
Identifieur interne : 001308 ( Istex/Corpus ); précédent : 001307; suivant : 001309Impact of Travel Between Patches for Spatial Spread of Disease
Auteurs : Ying-Hen Hsieh ; P. Van Den Driessche ; Lin WangSource :
- Bulletin of Mathematical Biology [ 0092-8240 ] ; 2007-05-01.
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Abstract
Abstract: A multipatch model is proposed to study the impact of travel on the spatial spread of disease between patches with different level of disease prevalence. The basic reproduction number for the ith patch in isolation is obtained along with the basic reproduction number of the system of patches, ℜ0. Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of ℜ0 on the travel rates between the two patches are obtained. For parameter values relevant for influenza, these results show that, while banning travel of infectives from the low to the high prevalence patch always contributes to disease control, banning travel of symptomatic travelers only from the high to the low prevalence patch could adversely affect the containment of the outbreak under certain ranges of parameter values. Moreover, banning all travel of infected individuals from the high to the low prevalence patch could result in the low prevalence patch becoming diseasefree, while the high prevalence patch becomes even more disease-prevalent, with the resulting number of infectives in this patch alone exceeding the combined number of infectives in both patches without border control. Under the set of parameter values used, our results demonstrate that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease between patches.
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DOI: 10.1007/s11538-006-9169-6
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Van Den Driessche</name><affiliation><mods:affiliation>Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: pvdd@math.uvic.ca</mods:affiliation></affiliation></author><author><name sortKey="Wang, Lin" sort="Wang, Lin" uniqKey="Wang L" first="Lin" last="Wang">Lin Wang</name><affiliation><mods:affiliation>Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada</mods:affiliation></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:1BD3B856DB981EBBB36EC2D98C96AF883FB5D07F</idno><date when="2007" year="2007">2007</date><idno type="doi">10.1007/s11538-006-9169-6</idno><idno type="url">https://api.istex.fr/ark:/67375/VQC-J0M5VX6T-F/fulltext.pdf</idno><idno type="wicri:Area/Istex/Corpus">001308</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001308</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">Impact of Travel Between Patches for Spatial Spread of Disease</title><author><name sortKey="Hsieh, Ying Hen" sort="Hsieh, Ying Hen" uniqKey="Hsieh Y" first="Ying-Hen" last="Hsieh">Ying-Hen Hsieh</name><affiliation><mods:affiliation>Department of Applied Mathematics, National Chung Hsing University, Taichung, Taiwan, R.O.C.</mods:affiliation></affiliation></author><author><name sortKey="Van Den Driessche, P" sort="Van Den Driessche, P" uniqKey="Van Den Driessche P" first="P." last="Van Den Driessche">P. Van Den Driessche</name><affiliation><mods:affiliation>Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: pvdd@math.uvic.ca</mods:affiliation></affiliation></author><author><name sortKey="Wang, Lin" sort="Wang, Lin" uniqKey="Wang L" first="Lin" last="Wang">Lin Wang</name><affiliation><mods:affiliation>Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j">Bulletin of Mathematical Biology</title><title level="j" type="sub">A Journal Devoted to Research at the Junction of Computational, Theoretical and Experimental BiologyOfficial Journal of The Society for Mathematical Biology</title><title level="j" type="abbrev">Bull. Math. Biol.</title><idno type="ISSN">0092-8240</idno><idno type="eISSN">1522-9602</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>New York</pubPlace><date type="published" when="2007-05-01">2007-05-01</date><biblScope unit="volume">69</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="page" from="1355">1355</biblScope><biblScope unit="page" to="1375">1375</biblScope></imprint><idno type="ISSN">0092-8240</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0092-8240</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Basic reproduction number</term><term>Border control</term><term>Influenza</term><term>Multipatch model</term><term>Spatial spread</term><term>Travel rate</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: A multipatch model is proposed to study the impact of travel on the spatial spread of disease between patches with different level of disease prevalence. The basic reproduction number for the ith patch in isolation is obtained along with the basic reproduction number of the system of patches, ℜ0. Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of ℜ0 on the travel rates between the two patches are obtained. For parameter values relevant for influenza, these results show that, while banning travel of infectives from the low to the high prevalence patch always contributes to disease control, banning travel of symptomatic travelers only from the high to the low prevalence patch could adversely affect the containment of the outbreak under certain ranges of parameter values. Moreover, banning all travel of infected individuals from the high to the low prevalence patch could result in the low prevalence patch becoming diseasefree, while the high prevalence patch becomes even more disease-prevalent, with the resulting number of infectives in this patch alone exceeding the combined number of infectives in both patches without border control. Under the set of parameter values used, our results demonstrate that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease between patches.</div></front></TEI><istex><corpusName>springer-journals</corpusName><author><json:item><name>Ying-Hen Hsieh</name><affiliations><json:string>Department of Applied Mathematics, National Chung Hsing University, Taichung, Taiwan, R.O.C.</json:string></affiliations></json:item><json:item><name>P. van den Driessche</name><affiliations><json:string>Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada</json:string><json:string>E-mail: pvdd@math.uvic.ca</json:string></affiliations></json:item><json:item><name>Lin Wang</name><affiliations><json:string>Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Basic reproduction number</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Border control</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Influenza</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Multipatch model</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Spatial spread</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Travel rate</value></json:item></subject><articleId><json:string>9169</json:string><json:string>s11538-006-9169-6</json:string></articleId><arkIstex>ark:/67375/VQC-J0M5VX6T-F</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>OriginalPaper</json:string></originalGenre><abstract>Abstract: A multipatch model is proposed to study the impact of travel on the spatial spread of disease between patches with different level of disease prevalence. The basic reproduction number for the ith patch in isolation is obtained along with the basic reproduction number of the system of patches, ℜ0. Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of ℜ0 on the travel rates between the two patches are obtained. For parameter values relevant for influenza, these results show that, while banning travel of infectives from the low to the high prevalence patch always contributes to disease control, banning travel of symptomatic travelers only from the high to the low prevalence patch could adversely affect the containment of the outbreak under certain ranges of parameter values. Moreover, banning all travel of infected individuals from the high to the low prevalence patch could result in the low prevalence patch becoming diseasefree, while the high prevalence patch becomes even more disease-prevalent, with the resulting number of infectives in this patch alone exceeding the combined number of infectives in both patches without border control. Under the set of parameter values used, our results demonstrate that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease between patches.</abstract><qualityIndicators><score>9.784</score><pdfWordCount>7264</pdfWordCount><pdfCharCount>34577</pdfCharCount><pdfVersion>1.3</pdfVersion><pdfPageCount>21</pdfPageCount><pdfPageSize>441 x 666 pts</pdfPageSize><refBibsNative>false</refBibsNative><abstractWordCount>232</abstractWordCount><abstractCharCount>1507</abstractCharCount><keywordCount>6</keywordCount></qualityIndicators><title>Impact of Travel Between Patches for Spatial Spread of Disease</title><genre><json:string>research-article</json:string></genre><host><title>Bulletin of Mathematical Biology</title><language><json:string>unknown</json:string></language><publicationDate>2007</publicationDate><copyrightDate>2007</copyrightDate><issn><json:string>0092-8240</json:string></issn><eissn><json:string>1522-9602</json:string></eissn><journalId><json:string>11538</json:string></journalId><volume>69</volume><issue>4</issue><pages><first>1355</first><last>1375</last></pages><genre><json:string>journal</json:string></genre><subject><json:item><value>Mathematical Biology in General</value></json:item></subject></host><ark><json:string>ark:/67375/VQC-J0M5VX6T-F</json:string></ark><publicationDate>2007</publicationDate><copyrightDate>2007</copyrightDate><doi><json:string>10.1007/s11538-006-9169-6</json:string></doi><id>1BD3B856DB981EBBB36EC2D98C96AF883FB5D07F</id><score>1</score><fulltext><json:item><extension>pdf</extension><original>true</original><mimetype>application/pdf</mimetype><uri>https://api.istex.fr/ark:/67375/VQC-J0M5VX6T-F/fulltext.pdf</uri></json:item><json:item><extension>zip</extension><original>false</original><mimetype>application/zip</mimetype><uri>https://api.istex.fr/ark:/67375/VQC-J0M5VX6T-F/bundle.zip</uri></json:item><istex:fulltextTEI uri="https://api.istex.fr/ark:/67375/VQC-J0M5VX6T-F/fulltext.tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main" xml:lang="en">Impact of Travel Between Patches for Spatial Spread of Disease</title></titleStmt><publicationStmt><authority>ISTEX</authority><publisher scheme="https://scientific-publisher.data.istex.fr">Springer-Verlag</publisher><pubPlace>New York</pubPlace><availability><licence><p>Springer Science+Business Media, Inc., 2007</p></licence><p scheme="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-3XSW68JL-F">springer</p></availability><date>2006-04-26</date></publicationStmt><notesStmt><note type="research-article" scheme="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</note><note type="journal" scheme="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</note><note>Original Article</note></notesStmt><sourceDesc><biblStruct type="inbook"><analytic><title level="a" type="main" xml:lang="en">Impact of Travel Between Patches for Spatial Spread of Disease</title><author xml:id="author-0000"><persName><forename type="first">Ying-Hen</forename><surname>Hsieh</surname></persName><affiliation>Department of Applied Mathematics, National Chung Hsing University, Taichung, Taiwan, R.O.C.</affiliation></author><author xml:id="author-0001" corresp="yes"><persName><forename type="first">P.</forename><surname>van den Driessche</surname></persName><email>pvdd@math.uvic.ca</email><affiliation>Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada</affiliation></author><author xml:id="author-0002"><persName><forename type="first">Lin</forename><surname>Wang</surname></persName><affiliation>Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada</affiliation></author><idno type="istex">1BD3B856DB981EBBB36EC2D98C96AF883FB5D07F</idno><idno type="ark">ark:/67375/VQC-J0M5VX6T-F</idno><idno type="DOI">10.1007/s11538-006-9169-6</idno><idno type="article-id">9169</idno><idno type="article-id">s11538-006-9169-6</idno></analytic><monogr><title level="j">Bulletin of Mathematical Biology</title><title level="j" type="sub">A Journal Devoted to Research at the Junction of Computational, Theoretical and Experimental BiologyOfficial Journal of The Society for Mathematical Biology</title><title level="j" type="abbrev">Bull. Math. Biol.</title><idno type="pISSN">0092-8240</idno><idno type="eISSN">1522-9602</idno><idno type="journal-ID">true</idno><idno type="issue-article-count">16</idno><idno type="volume-issue-count">8</idno><imprint><publisher>Springer-Verlag</publisher><pubPlace>New York</pubPlace><date type="published" when="2007-05-01"></date><biblScope unit="volume">69</biblScope><biblScope unit="issue">4</biblScope><biblScope unit="page" from="1355">1355</biblScope><biblScope unit="page" to="1375">1375</biblScope></imprint></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><creation><date>2006-04-26</date></creation><langUsage><language ident="en">en</language></langUsage><abstract xml:lang="en"><p>Abstract: A multipatch model is proposed to study the impact of travel on the spatial spread of disease between patches with different level of disease prevalence. The basic reproduction number for the ith patch in isolation is obtained along with the basic reproduction number of the system of patches, ℜ0. Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of ℜ0 on the travel rates between the two patches are obtained. For parameter values relevant for influenza, these results show that, while banning travel of infectives from the low to the high prevalence patch always contributes to disease control, banning travel of symptomatic travelers only from the high to the low prevalence patch could adversely affect the containment of the outbreak under certain ranges of parameter values. Moreover, banning all travel of infected individuals from the high to the low prevalence patch could result in the low prevalence patch becoming diseasefree, while the high prevalence patch becomes even more disease-prevalent, with the resulting number of infectives in this patch alone exceeding the combined number of infectives in both patches without border control. Under the set of parameter values used, our results demonstrate that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease between patches.</p></abstract><textClass xml:lang="en"><keywords scheme="keyword"><list><item><term>Basic reproduction number</term></item><item><term>Border control</term></item><item><term>Influenza</term></item><item><term>Multipatch model</term></item><item><term>Spatial spread</term></item><item><term>Travel rate</term></item></list></keywords></textClass><textClass><keywords scheme="Journal Subject"><list><head>Mathematics</head><item><term>Mathematical Biology in General</term></item></list></keywords></textClass></profileDesc><revisionDesc><change when="2006-04-26">Created</change><change when="2007-05-01">Published</change></revisionDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/ark:/67375/VQC-J0M5VX6T-F/fulltext.txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus springer-journals not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//Springer-Verlag//DTD A++ V2.4//EN" URI="http://devel.springer.de/A++/V2.4/DTD/A++V2.4.dtd" name="istex:docType"></istex:docType><istex:document><Publisher><PublisherInfo><PublisherName>Springer-Verlag</PublisherName><PublisherLocation>New York</PublisherLocation></PublisherInfo><Journal OutputMedium="All"><JournalInfo JournalProductType="ArchiveJournal" NumberingStyle="Unnumbered"><JournalID>11538</JournalID><JournalPrintISSN>0092-8240</JournalPrintISSN><JournalElectronicISSN>1522-9602</JournalElectronicISSN><JournalTitle>Bulletin of Mathematical Biology</JournalTitle><JournalSubTitle>A Journal Devoted to Research at the Junction of Computational, Theoretical and Experimental Biology
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The basic reproduction number for the <Emphasis Type="Italic">i</Emphasis>th patch in isolation is obtained along with the basic reproduction number of the system of patches, ℜ<Subscript>0</Subscript>. Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of ℜ<Subscript>0</Subscript> on the travel rates between the two patches are obtained. For parameter values relevant for influenza, these results show that, while banning travel of infectives from the low to the high prevalence patch always contributes to disease control, banning travel of symptomatic travelers only from the high to the low prevalence patch could adversely affect the containment of the outbreak under certain ranges of parameter values. Moreover, banning all travel of infected individuals from the high to the low prevalence patch could result in the low prevalence patch becoming diseasefree, while the high prevalence patch becomes even more disease-prevalent, with the resulting number of infectives in this patch alone exceeding the combined number of infectives in both patches without border control. Under the set of parameter values used, our results demonstrate that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease between patches.</Para></Abstract><KeywordGroup Language="En"><Keyword>Basic reproduction number</Keyword><Keyword>Border control</Keyword><Keyword>Influenza</Keyword><Keyword>Multipatch model</Keyword><Keyword>Spatial spread</Keyword><Keyword>Travel rate</Keyword></KeywordGroup></ArticleHeader><NoBody></NoBody></Article></Issue></Volume></Journal></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Impact of Travel Between Patches for Spatial Spread of Disease</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Impact of Travel Between Patches for Spatial Spread of Disease</title></titleInfo><name type="personal"><namePart type="given">Ying-Hen</namePart><namePart type="family">Hsieh</namePart><affiliation>Department of Applied Mathematics, National Chung Hsing University, Taichung, Taiwan, R.O.C.</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal" displayLabel="corresp"><namePart type="given">P.</namePart><namePart type="family">van den Driessche</namePart><affiliation>Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada</affiliation><affiliation>E-mail: pvdd@math.uvic.ca</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Lin</namePart><namePart type="family">Wang</namePart><affiliation>Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-1JC4F85T-7">research-article</genre><originInfo><publisher>Springer-Verlag</publisher><place><placeTerm type="text">New York</placeTerm></place><dateCreated encoding="w3cdtf">2006-04-26</dateCreated><dateIssued encoding="w3cdtf">2007-05-01</dateIssued><copyrightDate encoding="w3cdtf">2007</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: A multipatch model is proposed to study the impact of travel on the spatial spread of disease between patches with different level of disease prevalence. The basic reproduction number for the ith patch in isolation is obtained along with the basic reproduction number of the system of patches, ℜ0. Inequalities describing the relationship between these numbers are also given. For a two-patch model with one high prevalence patch and one low prevalence patch, results pertaining to the dependence of ℜ0 on the travel rates between the two patches are obtained. For parameter values relevant for influenza, these results show that, while banning travel of infectives from the low to the high prevalence patch always contributes to disease control, banning travel of symptomatic travelers only from the high to the low prevalence patch could adversely affect the containment of the outbreak under certain ranges of parameter values. Moreover, banning all travel of infected individuals from the high to the low prevalence patch could result in the low prevalence patch becoming diseasefree, while the high prevalence patch becomes even more disease-prevalent, with the resulting number of infectives in this patch alone exceeding the combined number of infectives in both patches without border control. Under the set of parameter values used, our results demonstrate that if border control is properly implemented, then it could contribute to stopping the spatial spread of disease between patches.</abstract><note>Original Article</note><subject lang="en"><topic>Basic reproduction number</topic><topic>Border control</topic><topic>Influenza</topic><topic>Multipatch model</topic><topic>Spatial spread</topic><topic>Travel rate</topic></subject><relatedItem type="host"><titleInfo><title>Bulletin of Mathematical Biology</title><subTitle>A Journal Devoted to Research at the Junction of Computational, Theoretical and Experimental BiologyOfficial Journal of The Society for Mathematical Biology</subTitle></titleInfo><titleInfo type="abbreviated"><title>Bull. Math. 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