Mathematical analysis of delay differential equation models of HIV-1 infection
Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays. We develop and analyze a set of models that include intracellular delays, combination antiretrovi...
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| Veröffentlicht in: | Mathematical biosciences 2002-07, Vol.179 (1), p.73-94 |
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| container_title | Mathematical biosciences |
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| creator | Nelson, Patrick W. Perelson, Alan S. |
| description | Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays. We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells. We show that when the drug efficacy is less than perfect the estimated value of the loss rate of productively infected T cells,
δ, is increased when data is fit with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of
δ. We also provide some general results on the stability of non-linear delay differential equation infection models. |
| doi_str_mv | 10.1016/S0025-5564(02)00099-8 |
| format | Article |
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δ, is increased when data is fit with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of
δ. We also provide some general results on the stability of non-linear delay differential equation infection models.</description><identifier>ISSN: 0025-5564</identifier><identifier>EISSN: 1879-3134</identifier><identifier>DOI: 10.1016/S0025-5564(02)00099-8</identifier><identifier>PMID: 12047922</identifier><identifier>CODEN: MABIAR</identifier><language>eng</language><publisher>New York, NY: Elsevier Inc</publisher><subject>Antiviral Agents - therapeutic use ; Biological and medical sciences ; Combination antiviral therapy ; Delay differential equations ; HIV Infections - drug therapy ; HIV Infections - immunology ; HIV Infections - virology ; HIV-1 ; Humans ; Medical sciences ; Models, Biological ; Numerical Analysis, Computer-Assisted ; Stability analysis ; T cells ; T-Lymphocytes - drug effects ; T-Lymphocytes - immunology ; Viral Load</subject><ispartof>Mathematical biosciences, 2002-07, Vol.179 (1), p.73-94</ispartof><rights>2002 Elsevier Science Inc.</rights><rights>2003 INIST-CNRS</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c540t-c2945d20f315ca3aa9c04fb590b4a1d481d37f47122afba58ca51a5985e651963</citedby><cites>FETCH-LOGICAL-c540t-c2945d20f315ca3aa9c04fb590b4a1d481d37f47122afba58ca51a5985e651963</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S0025556402000998$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>309,310,314,776,780,785,786,3536,23910,23911,25119,27903,27904,65309</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=13822326$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttps://www.ncbi.nlm.nih.gov/pubmed/12047922$$D View this record in MEDLINE/PubMed$$Hfree_for_read</backlink></links><search><creatorcontrib>Nelson, Patrick W.</creatorcontrib><creatorcontrib>Perelson, Alan S.</creatorcontrib><title>Mathematical analysis of delay differential equation models of HIV-1 infection</title><title>Mathematical biosciences</title><addtitle>Math Biosci</addtitle><description>Models of HIV-1 infection that include intracellular delays are more accurate representations of the biology and change the estimated values of kinetic parameters when compared to models without delays. We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells. We show that when the drug efficacy is less than perfect the estimated value of the loss rate of productively infected T cells,
δ, is increased when data is fit with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of
δ. 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We develop and analyze a set of models that include intracellular delays, combination antiretroviral therapy, and the dynamics of both infected and uninfected T cells. We show that when the drug efficacy is less than perfect the estimated value of the loss rate of productively infected T cells,
δ, is increased when data is fit with delay models compared to the values estimated with a non-delay model. We provide a mathematical justification for this increased value of
δ. We also provide some general results on the stability of non-linear delay differential equation infection models.</abstract><cop>New York, NY</cop><pub>Elsevier Inc</pub><pmid>12047922</pmid><doi>10.1016/S0025-5564(02)00099-8</doi><tpages>22</tpages></addata></record> |
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| ispartof | Mathematical biosciences, 2002-07, Vol.179 (1), p.73-94 |
| issn | 0025-5564 1879-3134 |
| language | eng |
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| source | MEDLINE; Elsevier ScienceDirect Journals |
| subjects | Antiviral Agents - therapeutic use Biological and medical sciences Combination antiviral therapy Delay differential equations HIV Infections - drug therapy HIV Infections - immunology HIV Infections - virology HIV-1 Humans Medical sciences Models, Biological Numerical Analysis, Computer-Assisted Stability analysis T cells T-Lymphocytes - drug effects T-Lymphocytes - immunology Viral Load |
| title | Mathematical analysis of delay differential equation models of HIV-1 infection |
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