Stability analysis of within-host parasite models with delays.
Identifieur interne : 000153 ( PubMed/Corpus ); précédent : 000152; suivant : 000154Stability analysis of within-host parasite models with delays.
Auteurs : Abderrahman Iggidr ; Joseph Mbang ; Gauthier SalletSource :
- Mathematical biosciences [ 0025-5564 ] ; 2007.
English descriptors
- KwdEn :
- MESH :
- microbiology : Infection.
- parasitology : Infection.
- physiology : HIV-1.
- virology : HIV Infections.
- Humans, Models, Biological.
Abstract
We provide a global analysis of systems of within-host parasitic infections. The systems studied have parallel classes of different length of latently infected target cells. These systems can also be thought as systems arising from within-host parasitic systems with distributed continuous delays. We compute the basic reproduction ratio R0 for the systems under consideration. If R0< or =1 the parasite is cleared, if R0>1 and if a sufficient condition is satisfied we conclude to the global asymptotic stability (GAS) of the endemic equilibrium. For some generic class of models this condition reduces to R0>1. These results make possible to revisit some parasitic models including intracellular delays and to study their global stability.
DOI: 10.1016/j.mbs.2007.01.008
PubMed: 17383688
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pubmed:17383688Le document en format XML
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A, Ile du Saulcy 57045 Metz Cedex 01, France. iggidr@loria.fr</nlm:affiliation></affiliation></author><author><name sortKey="Mbang, Joseph" sort="Mbang, Joseph" uniqKey="Mbang J" first="Joseph" last="Mbang">Joseph Mbang</name></author><author><name sortKey="Sallet, Gauthier" sort="Sallet, Gauthier" uniqKey="Sallet G" first="Gauthier" last="Sallet">Gauthier Sallet</name></author></titleStmt><publicationStmt><idno type="wicri:source">PubMed</idno><date when="2007">2007</date><idno type="doi">10.1016/j.mbs.2007.01.008</idno><idno type="RBID">pubmed:17383688</idno><idno type="pmid">17383688</idno><idno type="wicri:Area/PubMed/Corpus">000153</idno><idno type="wicri:explorRef" wicri:stream="PubMed" wicri:step="Corpus" wicri:corpus="PubMed">000153</idno></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en">Stability analysis of within-host parasite models with delays.</title><author><name sortKey="Iggidr, Abderrahman" sort="Iggidr, Abderrahman" uniqKey="Iggidr A" first="Abderrahman" last="Iggidr">Abderrahman Iggidr</name><affiliation><nlm:affiliation>INRIA-Lorraine and University Paul Verlaine-Metz LMAM-CNRS UMR 7122, ISGMP Bat. A, Ile du Saulcy 57045 Metz Cedex 01, France. iggidr@loria.fr</nlm:affiliation></affiliation></author><author><name sortKey="Mbang, Joseph" sort="Mbang, Joseph" uniqKey="Mbang J" first="Joseph" last="Mbang">Joseph Mbang</name></author><author><name sortKey="Sallet, Gauthier" sort="Sallet, Gauthier" uniqKey="Sallet G" first="Gauthier" last="Sallet">Gauthier Sallet</name></author></analytic><series><title level="j">Mathematical biosciences</title><idno type="ISSN">0025-5564</idno><imprint><date when="2007" type="published">2007</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>HIV Infections (virology)</term><term>HIV-1 (physiology)</term><term>Humans</term><term>Infection (microbiology)</term><term>Infection (parasitology)</term><term>Models, Biological</term></keywords><keywords scheme="MESH" qualifier="microbiology" xml:lang="en"><term>Infection</term></keywords><keywords scheme="MESH" qualifier="parasitology" xml:lang="en"><term>Infection</term></keywords><keywords scheme="MESH" qualifier="physiology" xml:lang="en"><term>HIV-1</term></keywords><keywords scheme="MESH" qualifier="virology" xml:lang="en"><term>HIV Infections</term></keywords><keywords scheme="MESH" xml:lang="en"><term>Humans</term><term>Models, Biological</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">We provide a global analysis of systems of within-host parasitic infections. The systems studied have parallel classes of different length of latently infected target cells. These systems can also be thought as systems arising from within-host parasitic systems with distributed continuous delays. We compute the basic reproduction ratio R0 for the systems under consideration. If R0< or =1 the parasite is cleared, if R0>1 and if a sufficient condition is satisfied we conclude to the global asymptotic stability (GAS) of the endemic equilibrium. For some generic class of models this condition reduces to R0>1. These results make possible to revisit some parasitic models including intracellular delays and to study their global stability.</div></front></TEI><pubmed><MedlineCitation Owner="NLM" Status="MEDLINE"><PMID Version="1">17383688</PMID><DateCreated><Year>2007</Year><Month>08</Month><Day>16</Day></DateCreated><DateCompleted><Year>2007</Year><Month>11</Month><Day>08</Day></DateCompleted><DateRevised><Year>2009</Year><Month>11</Month><Day>11</Day></DateRevised><Article PubModel="Print-Electronic"><Journal><ISSN IssnType="Print">0025-5564</ISSN><JournalIssue CitedMedium="Print"><Volume>209</Volume><Issue>1</Issue><PubDate><Year>2007</Year><Month>Sep</Month></PubDate></JournalIssue><Title>Mathematical biosciences</Title><ISOAbbreviation>Math Biosci</ISOAbbreviation></Journal><ArticleTitle>Stability analysis of within-host parasite models with delays.</ArticleTitle><Pagination><MedlinePgn>51-75</MedlinePgn></Pagination><Abstract><AbstractText>We provide a global analysis of systems of within-host parasitic infections. The systems studied have parallel classes of different length of latently infected target cells. These systems can also be thought as systems arising from within-host parasitic systems with distributed continuous delays. We compute the basic reproduction ratio R0 for the systems under consideration. If R0< or =1 the parasite is cleared, if R0>1 and if a sufficient condition is satisfied we conclude to the global asymptotic stability (GAS) of the endemic equilibrium. For some generic class of models this condition reduces to R0>1. These results make possible to revisit some parasitic models including intracellular delays and to study their global stability.</AbstractText></Abstract><AuthorList CompleteYN="Y"><Author ValidYN="Y"><LastName>Iggidr</LastName><ForeName>Abderrahman</ForeName><Initials>A</Initials><AffiliationInfo><Affiliation>INRIA-Lorraine and University Paul Verlaine-Metz LMAM-CNRS UMR 7122, ISGMP Bat. A, Ile du Saulcy 57045 Metz Cedex 01, France. iggidr@loria.fr</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Mbang</LastName><ForeName>Joseph</ForeName><Initials>J</Initials></Author><Author ValidYN="Y"><LastName>Sallet</LastName><ForeName>Gauthier</ForeName><Initials>G</Initials></Author></AuthorList><Language>eng</Language><PublicationTypeList><PublicationType UI="D016428">Journal Article</PublicationType></PublicationTypeList><ArticleDate DateType="Electronic"><Year>2007</Year><Month>02</Month><Day>09</Day></ArticleDate></Article><MedlineJournalInfo><Country>United States</Country><MedlineTA>Math Biosci</MedlineTA><NlmUniqueID>0103146</NlmUniqueID><ISSNLinking>0025-5564</ISSNLinking></MedlineJournalInfo><CitationSubset>IM</CitationSubset><MeshHeadingList><MeshHeading><DescriptorName MajorTopicYN="N" UI="D015658">HIV Infections</DescriptorName><QualifierName MajorTopicYN="N" UI="Q000821">virology</QualifierName></MeshHeading><MeshHeading><DescriptorName MajorTopicYN="N" UI="D015497">HIV-1</DescriptorName><QualifierName MajorTopicYN="N" UI="Q000502">physiology</QualifierName></MeshHeading><MeshHeading><DescriptorName MajorTopicYN="N" UI="D006801">Humans</DescriptorName></MeshHeading><MeshHeading><DescriptorName MajorTopicYN="N" UI="D007239">Infection</DescriptorName><QualifierName MajorTopicYN="Y" UI="Q000382">microbiology</QualifierName><QualifierName MajorTopicYN="Y" UI="Q000469">parasitology</QualifierName></MeshHeading><MeshHeading><DescriptorName MajorTopicYN="Y" UI="D008954">Models, Biological</DescriptorName></MeshHeading></MeshHeadingList></MedlineCitation><PubmedData><History><PubMedPubDate PubStatus="received"><Year>2006</Year><Month>4</Month><Day>12</Day></PubMedPubDate><PubMedPubDate PubStatus="revised"><Year>2006</Year><Month>12</Month><Day>12</Day></PubMedPubDate><PubMedPubDate PubStatus="accepted"><Year>2007</Year><Month>1</Month><Day>16</Day></PubMedPubDate><PubMedPubDate PubStatus="aheadofprint"><Year>2007</Year><Month>2</Month><Day>9</Day></PubMedPubDate><PubMedPubDate PubStatus="pubmed"><Year>2007</Year><Month>3</Month><Day>27</Day><Hour>9</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="medline"><Year>2007</Year><Month>11</Month><Day>9</Day><Hour>9</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="entrez"><Year>2007</Year><Month>3</Month><Day>27</Day><Hour>9</Hour><Minute>0</Minute></PubMedPubDate></History><PublicationStatus>ppublish</PublicationStatus><ArticleIdList><ArticleId IdType="pii">S0025-5564(07)00011-9</ArticleId><ArticleId IdType="doi">10.1016/j.mbs.2007.01.008</ArticleId><ArticleId IdType="pubmed">17383688</ArticleId></ArticleIdList></PubmedData></pubmed></record>Pour manipuler ce document sous Unix (Dilib)
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