Memory Effects in Population Dynamics : Spread of Infectious Disease as a Case Study
Identifieur interne : 001C15 ( Istex/Corpus ); précédent : 001C14; suivant : 001C16Memory Effects in Population Dynamics : Spread of Infectious Disease as a Case Study
Auteurs : A. Pimenov ; T. C. Kelly ; A. Korobeinikov ; M. J. A. O Allaghan ; A. V. Pokrovskii ; D. RachinskiiSource :
- Mathematical Modelling of Natural Phenomena [ 0973-5348 ] ; 2012-06-06.
Abstract
Modification of behaviour in response to changes in the environment or ambient conditions, based on memory, is typical of the human and, possibly, many animal species.One obvious example of such adaptivity is, for instance, switching to a safer behaviour when in danger, from either a predator or an infectious disease. In human society such switching to safe behaviour is particularly apparent during epidemics. Mathematically, such changes of behaviour in response to changes in the ambient conditions can be described by models involving switching. In most cases, this switching is assumed to depend on the system state, and thus it disregards the history and, therefore, memory. Memory can be introduced into a mathematical model using a phenomenon known as hysteresis. We illustrate this idea using a simple SIR compartmental model that is applicable in epidemiology. Our goal is to show why and how hysteresis can arise in such a model, and how it may be applied to describe a variety of memory effects. Our other objective is to introduce a unified paradigm for mathematical modelling with memory effects in epidemiology and ecology. Our approach treats changing behaviour as an irreversible flow related to large ensembles of elementary exchange operations that recently has been successfully applied in a number of other areas, such as terrestrial hydrology, and macroeconomics. For the purposes of illustrating these ideas in an application to biology, we consider a rather simple case study and develop a model from first principles. We accompany the model with extensive numerical simulations which exhibit interesting qualitative effects.
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DOI: 10.1051/mmnp/20127313
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Korobeinikov</name><affiliation><mods:affiliation>MACSI, Department of Mathematics and Statistics, University of Limerick, Ireland</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: andrei.korobeinikov@ul.ie</mods:affiliation></affiliation></author><author><name sortKey="O Allaghan, M J A" sort="O Allaghan, M J A" uniqKey="O Allaghan M" first="M. J. A." last="O Allaghan">M. J. A. O Allaghan</name><affiliation><mods:affiliation>Department of Applied Mathematics, University College Cork, Ireland</mods:affiliation></affiliation></author><author><name sortKey="Pokrovskii, A V" sort="Pokrovskii, A V" uniqKey="Pokrovskii A" first="A. V." last="Pokrovskii">A. V. Pokrovskii</name><affiliation><mods:affiliation>Department of Applied Mathematics, University College Cork, Ireland</mods:affiliation></affiliation></author><author><name sortKey="Rachinskii, D" sort="Rachinskii, D" uniqKey="Rachinskii D" first="D." last="Rachinskii">D. Rachinskii</name><affiliation><mods:affiliation>Department of Applied Mathematics, University College Cork, Ireland</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j" type="main">Mathematical Modelling of Natural Phenomena</title><title level="j" type="issue">Epidemiology</title><title level="j" type="abbrev">Math. Model. Nat. Phenom.</title><title level="j" type="publisher-id">mmnp</title><idno type="ISSN">0973-5348</idno><idno type="eISSN">1760-6101</idno><imprint><publisher>EDP Sciences</publisher><date type="Final-Published" when="2012-06-06">2012-06-06</date><date type="ePublished" when="2012-06-06">2012-06-06</date><date type="Published" when="2012">2012</date><biblScope unit="vol">7</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="204">204</biblScope><biblScope unit="page" to="226">226</biblScope><biblScope unit="page-count">23</biblScope><biblScope unit="ref-count">79</biblScope></imprint><idno type="ISSN">0973-5348</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0973-5348</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Modification of behaviour in response to changes in the environment or ambient conditions, based on memory, is typical of the human and, possibly, many animal species.One obvious example of such adaptivity is, for instance, switching to a safer behaviour when in danger, from either a predator or an infectious disease. In human society such switching to safe behaviour is particularly apparent during epidemics. Mathematically, such changes of behaviour in response to changes in the ambient conditions can be described by models involving switching. In most cases, this switching is assumed to depend on the system state, and thus it disregards the history and, therefore, memory. Memory can be introduced into a mathematical model using a phenomenon known as hysteresis. We illustrate this idea using a simple SIR compartmental model that is applicable in epidemiology. Our goal is to show why and how hysteresis can arise in such a model, and how it may be applied to describe a variety of memory effects. Our other objective is to introduce a unified paradigm for mathematical modelling with memory effects in epidemiology and ecology. Our approach treats changing behaviour as an irreversible flow related to large ensembles of elementary exchange operations that recently has been successfully applied in a number of other areas, such as terrestrial hydrology, and macroeconomics. For the purposes of illustrating these ideas in an application to biology, we consider a rather simple case study and develop a model from first principles. We accompany the model with extensive numerical simulations which exhibit interesting qualitative effects.</div></front></TEI><istex><corpusName>edp-sciences</corpusName><author><json:item><name>A. Pimenov</name><affiliations><json:string>Weierstrass Institute, Mohrenstrasse 39, D-10117 Berlin, Germany</json:string></affiliations></json:item><json:item><name>T.C. Kelly</name><affiliations><json:string>Department of Biology, Earth and Environmental Science, University College Cork, Ireland</json:string></affiliations></json:item><json:item><name>A. 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In human society such switching to safe behaviour is particularly apparent during epidemics. Mathematically, such changes of behaviour in response to changes in the ambient conditions can be described by models involving switching. In most cases, this switching is assumed to depend on the system state, and thus it disregards the history and, therefore, memory. Memory can be introduced into a mathematical model using a phenomenon known as hysteresis. We illustrate this idea using a simple SIR compartmental model that is applicable in epidemiology. Our goal is to show why and how hysteresis can arise in such a model, and how it may be applied to describe a variety of memory effects. Our other objective is to introduce a unified paradigm for mathematical modelling with memory effects in epidemiology and ecology. Our approach treats changing behaviour as an irreversible flow related to large ensembles of elementary exchange operations that recently has been successfully applied in a number of other areas, such as terrestrial hydrology, and macroeconomics. For the purposes of illustrating these ideas in an application to biology, we consider a rather simple case study and develop a model from first principles. 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Disease as a Case Study</title><author xml:id="author-0000"><persName><surname>Pimenov</surname><forename type="first">A.</forename></persName><affiliation><orgName type="institution">Weierstrass Institute</orgName><address><street>Mohrenstrasse 39</street><postCode>D-10117</postCode><settlement>Berlin</settlement><country key="DE">Germany</country></address></affiliation></author><author xml:id="author-0001"><persName><surname>Kelly</surname><forename type="first">T.C.</forename></persName><affiliation><orgName type="institution">Department of Biology, Earth and Environmental Science, University
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College Cork</orgName></affiliation></author><idno type="istex">F775B40CF3FC7718EF9763325049E84D4D2FC996</idno><idno type="ark">ark:/67375/80W-KC3653JC-7</idno><idno type="DOI">10.1051/mmnp/20127313</idno><idno type="publisher-id">mmnp201273p204</idno><idno type="PII">S0973534812073130</idno></analytic><monogr><title level="j" type="main">Mathematical Modelling of Natural Phenomena</title><title level="j" type="issue">Epidemiology</title><title level="j" type="abbrev">Math. Model. Nat. Phenom.</title><title level="j" type="publisher-id">mmnp</title><idno type="pISSN">0973-5348</idno><idno type="eISSN">1760-6101</idno><imprint><publisher>EDP Sciences</publisher><date type="Final-Published" when="2012-06-06"></date><date type="ePublished" when="2012-06-06"></date><date type="Published" when="2012"></date><biblScope unit="vol">7</biblScope><biblScope unit="issue">3</biblScope><biblScope unit="page" from="204">204</biblScope><biblScope unit="page" to="226">226</biblScope><biblScope unit="page-count">23</biblScope><biblScope unit="ref-count">79</biblScope></imprint></monogr></biblStruct></sourceDesc></fileDesc><profileDesc><abstract xml:lang="en"><p>Modification of behaviour in response to changes in the environment or ambient
conditions, based on memory, is typical of the human and, possibly, many animal
species.One obvious example of such adaptivity is, for instance, switching to a safer
behaviour when in danger, from either a predator or an infectious disease. In human
society such switching to safe behaviour is particularly apparent during epidemics.
Mathematically, such changes of behaviour in response to changes in the ambient conditions
can be described by models involving switching. In most cases, this switching is assumed
to depend on the system state, and thus it disregards the history and, therefore, memory.
Memory can be introduced into a mathematical model using a phenomenon known as hysteresis.
We illustrate this idea using a simple SIR compartmental model that is applicable in
epidemiology. Our goal is to show why and how hysteresis can arise in such a model, and
how it may be applied to describe a variety of memory effects. Our other objective is to
introduce a unified paradigm for mathematical modelling with memory effects in
epidemiology and ecology. Our approach treats changing behaviour as an irreversible flow
related to large ensembles of elementary exchange operations that recently has been
successfully applied in a number of other areas, such as terrestrial hydrology, and
macroeconomics. For the purposes of illustrating these ideas in an application to biology,
we consider a rather simple case study and develop a model from first principles. We
accompany the model with extensive numerical simulations which exhibit interesting
qualitative effects.</p></abstract><textClass><keywords xml:lang="en"><term>mathematical epidemiology</term><term>SIR model</term><term>hysteresis</term><term>PETS</term><term>adaptation</term><term>memory effects</term><term>equilibrium</term><term>infectious disease</term><term>Preisach operator</term><term>operator-differential equations</term><term>dynamics</term><term>public information</term><term>olfactory</term></keywords></textClass><textClass><keywords scheme="AMS Code" xml:lang="en"><list><item><label>92D30</label></item><item><label>47J40</label></item></list></keywords></textClass><langUsage><language ident="en"></language></langUsage></profileDesc></teiHeader></istex:fulltextTEI><json:item><extension>txt</extension><original>false</original><mimetype>text/plain</mimetype><uri>https://api.istex.fr/ark:/67375/80W-KC3653JC-7/fulltext.txt</uri></json:item></fulltext><metadata><istex:metadataXml wicri:clean="corpus edp-sciences not found" wicri:toSee="no header"><istex:xmlDeclaration>version="1.0" encoding="UTF-8"</istex:xmlDeclaration><istex:docType PUBLIC="-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.0 20120330//EN" URI="JATS-journalpublishing1.dtd" name="istex:docType"></istex:docType><istex:document><article article-type="research-article" dtd-version="1.0" xml:lang="en"><front><!-- À placer dans le répertoire contenant les issues de la revue :
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--><journal-meta><journal-id journal-id-type="publisher-id">mmnp</journal-id><journal-title-group><journal-title>Mathematical Modelling of Natural Phenomena</journal-title><abbrev-journal-title abbrev-type="publisher">Math. Model. Nat. Phenom.</abbrev-journal-title></journal-title-group><issn pub-type="ppub">0973-5348</issn><issn pub-type="epub">1760-6101</issn><publisher><publisher-name>EDP Sciences</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="doi">10.1051/mmnp/20127313</article-id><article-id pub-id-type="publisher-id">mmnp201273p204</article-id><article-id pub-id-type="pii">S0973534812073130</article-id><title-group><article-title xml:lang="en">Memory Effects in Population Dynamics : Spread of Infectious
Disease as a Case Study</article-title></title-group><contrib-group><contrib contrib-type="author"><name><surname>Pimenov</surname><given-names>A.</given-names></name><xref ref-type="aff" rid="AFF1">1</xref></contrib><contrib contrib-type="author"><name><surname>Kelly</surname><given-names>T.C.</given-names></name><xref ref-type="aff" rid="AFF2">2</xref></contrib><contrib contrib-type="author" corresp="yes"><name><surname>Korobeinikov</surname><given-names>A.</given-names></name><xref ref-type="aff" rid="AFF3">3</xref><xref ref-type="corresp" rid="FN1">⋆</xref></contrib><contrib contrib-type="author"><name><surname>O’Callaghan</surname><given-names>M.J.A.</given-names></name><xref ref-type="aff" rid="AFF4">4</xref></contrib><contrib contrib-type="author"><name><surname>Pokrovskii</surname><given-names>A.V.</given-names></name><xref ref-type="aff" rid="AFF4">4</xref></contrib><contrib contrib-type="author"><name><surname>Rachinskii</surname><given-names>D.</given-names></name><xref ref-type="aff" rid="AFF4">4</xref></contrib><aff id="AFF1"><label>1</label><addr-line><institution>Weierstrass Institute</institution>, <named-content content-type="street">Mohrenstrasse 39</named-content>, <named-content content-type="postcode">D-10117</named-content><named-content content-type="city">Berlin</named-content>,
<country>Germany</country></addr-line></aff><aff id="AFF2"><label>2</label><addr-line><institution>Department of Biology, Earth and Environmental Science, University
College Cork</institution>, <country>Ireland</country></addr-line></aff><aff id="AFF3"><label>3</label><institution>MACSI, Department of Mathematics and Statistics,
University of Limerick</institution>, <country>Ireland</country></aff><aff id="AFF4"><label>4</label><institution>Department of Applied Mathematics, University
College Cork</institution>, <country>Ireland</country></aff></contrib-group><author-notes><corresp id="FN1"><label>⋆</label> Corresponding author. E-mail: <email>andrei.korobeinikov@ul.ie</email></corresp></author-notes><pub-date pub-type="final"><day>06</day><month>06</month><year>2012</year></pub-date><pub-date pub-type="epub"><day>06</day><month>06</month><year>2012</year></pub-date><!-- à changer tous les ans !! --><pub-date pub-type="ppub"><year>2012</year></pub-date><volume>7</volume><issue>3</issue><issue-id pub-id-type="publisher-id">mmnp/2012/03</issue-id><issue-title>Epidemiology</issue-title><fpage>204</fpage><lpage>226</lpage><permissions><copyright-statement>© EDP Sciences, 2012</copyright-statement><copyright-year>2012</copyright-year><copyright-holder>EDP Sciences</copyright-holder></permissions><abstract xml:lang="en"><p>Modification of behaviour in response to changes in the environment or ambient
conditions, based on memory, is typical of the human and, possibly, many animal
species.One obvious example of such adaptivity is, for instance, switching to a safer
behaviour when in danger, from either a predator or an infectious disease. In human
society such switching to safe behaviour is particularly apparent during epidemics.
Mathematically, such changes of behaviour in response to changes in the ambient conditions
can be described by models involving switching. In most cases, this switching is assumed
to depend on the system state, and thus it disregards the history and, therefore, memory.
Memory can be introduced into a mathematical model using a phenomenon known as hysteresis.
We illustrate this idea using a simple SIR compartmental model that is applicable in
epidemiology. Our goal is to show why and how hysteresis can arise in such a model, and
how it may be applied to describe a variety of memory effects. Our other objective is to
introduce a unified paradigm for mathematical modelling with memory effects in
epidemiology and ecology. Our approach treats changing behaviour as an irreversible flow
related to large ensembles of elementary exchange operations that recently has been
successfully applied in a number of other areas, such as terrestrial hydrology, and
macroeconomics. For the purposes of illustrating these ideas in an application to biology,
we consider a rather simple case study and develop a model from first principles. We
accompany the model with extensive numerical simulations which exhibit interesting
qualitative effects.</p></abstract><kwd-group xml:lang="en"><kwd>mathematical epidemiology</kwd><kwd>SIR model</kwd><kwd>hysteresis</kwd><kwd>PETS</kwd><kwd>adaptation</kwd><kwd>memory effects</kwd><kwd>equilibrium</kwd><kwd>infectious disease</kwd><kwd>Preisach operator</kwd><kwd>operator-differential equations</kwd><kwd>dynamics</kwd><kwd>public information</kwd><kwd>olfactory</kwd></kwd-group><kwd-group xml:lang="en" kwd-group-type="AMS Code"><compound-kwd><compound-kwd-part content-type="code">92D30</compound-kwd-part></compound-kwd><compound-kwd><compound-kwd-part content-type="code">47J40</compound-kwd-part></compound-kwd></kwd-group><counts><ref-count count="79"></ref-count><page-count count="23"></page-count></counts><custom-meta-group><custom-meta><meta-name>idline</meta-name><meta-value><italic>Math. Model. Nat. Phenom. </italic>Vol. 7, No. 3, 2012, pp. 204-226</meta-value></custom-meta><custom-meta><!-- xml_type : si 'header', le body sera supprimé --><meta-name>xml_type</meta-name><meta-value>header</meta-value></custom-meta><custom-meta><meta-name>cover_date</meta-name><meta-value>2012</meta-value></custom-meta><custom-meta><meta-name>first_year</meta-name><meta-value>2012</meta-value></custom-meta><custom-meta><meta-name>last_year</meta-name><meta-value>2012</meta-value></custom-meta></custom-meta-group></article-meta></front><back><ref-list><title>References</title><!--LaTeX original ID: Amoetal2008--><ref id="R1"><mixed-citation publication-type="journal"><string-name><given-names>L.</given-names><surname>Amo</surname></string-name>, <string-name><given-names>I.</given-names><surname>Galván</surname></string-name>, <string-name><given-names>G.</given-names><surname>Tomás</surname></string-name>, <string-name><given-names>J.J.</given-names><surname>Sanz</surname></string-name>, <article-title><italic>Predator odour recognition
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</mixed-citation></ref></ref-list></back></article></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Memory Effects in Population Dynamics : Spread of Infectious Disease as a Case Study</title></titleInfo><titleInfo type="alternative" lang="en" contentType="CDATA"><title>Memory Effects in Population Dynamics : Spread of Infectious Disease as a Case Study</title></titleInfo><name type="personal"><namePart type="given">A.</namePart><namePart type="family">Pimenov</namePart><affiliation>Weierstrass Institute, Mohrenstrasse 39, D-10117 Berlin, Germany</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">T.C.</namePart><namePart type="family">Kelly</namePart><affiliation>Department of Biology, Earth and Environmental Science, University College Cork, Ireland</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal" displayLabel="corresp"><namePart type="given">A.</namePart><namePart type="family">Korobeinikov</namePart><affiliation>MACSI, Department of Mathematics and Statistics, University of Limerick, Ireland</affiliation><affiliation>E-mail: andrei.korobeinikov@ul.ie</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M.J.A.</namePart><namePart type="family">O’Callaghan</namePart><affiliation>Department of Applied Mathematics, University College Cork, Ireland</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">A.V.</namePart><namePart type="family">Pokrovskii</namePart><affiliation>Department of Applied Mathematics, University College Cork, Ireland</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">D.</namePart><namePart type="family">Rachinskii</namePart><affiliation>Department of Applied Mathematics, University College Cork, Ireland</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre type="research-article" displayLabel="research-article" 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>EDP Sciences</publisher><dateIssued encoding="w3cdtf">2012</dateIssued><dateCreated encoding="w3cdtf">2012-06-06</dateCreated><copyrightDate encoding="w3cdtf">2012</copyrightDate></originInfo><language><languageTerm type="code" authority="iso639-2b">eng</languageTerm><languageTerm type="code" authority="rfc3066">en</languageTerm></language><physicalDescription><extent unit="references">79</extent></physicalDescription><abstract lang="en">Modification of behaviour in response to changes in the environment or ambient conditions, based on memory, is typical of the human and, possibly, many animal species.One obvious example of such adaptivity is, for instance, switching to a safer behaviour when in danger, from either a predator or an infectious disease. In human society such switching to safe behaviour is particularly apparent during epidemics. Mathematically, such changes of behaviour in response to changes in the ambient conditions can be described by models involving switching. In most cases, this switching is assumed to depend on the system state, and thus it disregards the history and, therefore, memory. Memory can be introduced into a mathematical model using a phenomenon known as hysteresis. We illustrate this idea using a simple SIR compartmental model that is applicable in epidemiology. Our goal is to show why and how hysteresis can arise in such a model, and how it may be applied to describe a variety of memory effects. Our other objective is to introduce a unified paradigm for mathematical modelling with memory effects in epidemiology and ecology. Our approach treats changing behaviour as an irreversible flow related to large ensembles of elementary exchange operations that recently has been successfully applied in a number of other areas, such as terrestrial hydrology, and macroeconomics. For the purposes of illustrating these ideas in an application to biology, we consider a rather simple case study and develop a model from first principles. We accompany the model with extensive numerical simulations which exhibit interesting qualitative effects.</abstract><subject lang="en"><genre>keywords</genre><topic>mathematical epidemiology</topic><topic>SIR model</topic><topic>hysteresis</topic><topic>PETS</topic><topic>adaptation</topic><topic>memory effects</topic><topic>equilibrium</topic><topic>infectious disease</topic><topic>Preisach operator</topic><topic>operator-differential equations</topic><topic>dynamics</topic><topic>public information</topic><topic>olfactory</topic></subject><subject lang="en"><genre>AMS Code</genre><topic authority="AMS-Code">92D30</topic><topic authority="AMS-Code">47J40</topic></subject><relatedItem type="host"><titleInfo><title>Mathematical Modelling of Natural Phenomena</title></titleInfo><genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre><identifier type="ISSN">0973-5348</identifier><identifier type="eISSN">1760-6101</identifier><identifier type="PublisherID">mmnp</identifier><part><date>2012</date><detail type="title"><title>Epidemiology</title></detail><detail type="volume"><caption>vol.</caption><number>7</number></detail><detail type="issue"><caption>no.</caption><number>3</number></detail><extent unit="pages"><start>204</start><end>226</end><total>23</total></extent></part></relatedItem><identifier type="istex">F775B40CF3FC7718EF9763325049E84D4D2FC996</identifier><identifier type="ark">ark:/67375/80W-KC3653JC-7</identifier><identifier type="DOI">10.1051/mmnp/20127313</identifier><identifier type="publisher-ID">mmnp201273p204</identifier><identifier type="PII">S0973534812073130</identifier><accessCondition type="use and reproduction" contentType="copyright">© EDP Sciences, 2012</accessCondition><recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-00BJNC61-D">EDP</recordContentSource><recordOrigin>© EDP Sciences, 2012</recordOrigin></recordInfo></mods><json:item><extension>json</extension><original>false</original><mimetype>application/json</mimetype><uri>https://api.istex.fr/ark:/67375/80W-KC3653JC-7/record.json</uri></json:item></metadata><serie></serie></istex></record>Pour manipuler ce document sous Unix (Dilib)
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