Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review
Identifieur interne : 000269 ( Ncbi/Merge ); précédent : 000268; suivant : 000270Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review
Auteurs : Pablo S. Rivadeneira ; Claude H. Moog ; Guy-Bart Stan ; Cecile Brunet ; François Raffi ; Virginie Ferré ; Vicente Costanza ; Marie J. Mhawej ; Federico Biafore ; Djomangan A. Ouattara ; Damien Ernst ; Raphael Fonteneau ; Xiaohua XiaSource :
- BioResearch Open Access [ 2164-7844 ] ; 2014.
Abstract
This review shows the potential ground-breaking impact that mathematical tools may have in the analysis and the understanding of the HIV dynamics. In the first part, early diagnosis of immunological failure is inferred from the estimation of certain parameters of a mathematical model of the HIV infection dynamics. This method is supported by clinical research results from an original clinical trial: data just after 1 month following therapy initiation are used to carry out the model identification. The diagnosis is shown to be consistent with results from monitoring of the patients after 6 months. In the second part of this review, prospective research results are given for the design of individual anti-HIV treatments optimizing the recovery of the immune system and minimizing side effects. In this respect, two methods are discussed. The first one combines HIV population dynamics with pharmacokinetics and pharmacodynamics models to generate drug treatments using impulsive control systems. The second one is based on optimal control theory and uses a recently published differential equation to model the side effects produced by highly active antiretroviral therapy therapies. The main advantage of these revisited methods is that the drug treatment is computed directly in amounts of drugs, which is easier to interpret by physicians and patients.
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DOI: 10.1089/biores.2014.0024
PubMed: 25371860
PubMed Central: 4215334
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Moog</name><affiliation><nlm:aff id="aff2"></nlm:aff></affiliation></author><author><name sortKey="Stan, Guy Bart" sort="Stan, Guy Bart" uniqKey="Stan G" first="Guy-Bart" last="Stan">Guy-Bart Stan</name><affiliation><nlm:aff id="aff3"></nlm:aff></affiliation></author><author><name sortKey="Brunet, Cecile" sort="Brunet, Cecile" uniqKey="Brunet C" first="Cecile" last="Brunet">Cecile Brunet</name><affiliation><nlm:aff id="aff4"></nlm:aff></affiliation><affiliation><nlm:aff id="aff5"></nlm:aff></affiliation></author><author><name sortKey="Raffi, Francois" sort="Raffi, Francois" uniqKey="Raffi F" first="François" last="Raffi">François Raffi</name><affiliation><nlm:aff id="aff4"></nlm:aff></affiliation><affiliation><nlm:aff id="aff5"></nlm:aff></affiliation></author><author><name sortKey="Ferre, Virginie" sort="Ferre, Virginie" uniqKey="Ferre V" first="Virginie" last="Ferré">Virginie Ferré</name><affiliation><nlm:aff id="aff4"></nlm:aff></affiliation><affiliation><nlm:aff id="aff5"></nlm:aff></affiliation></author><author><name sortKey="Costanza, Vicente" sort="Costanza, Vicente" uniqKey="Costanza V" first="Vicente" last="Costanza">Vicente Costanza</name><affiliation><nlm:aff id="aff1"></nlm:aff></affiliation></author><author><name sortKey="Mhawej, Marie J" sort="Mhawej, Marie J" uniqKey="Mhawej M" first="Marie J." last="Mhawej">Marie J. 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Rivadeneira</name><affiliation><nlm:aff id="aff1"></nlm:aff></affiliation><affiliation><nlm:aff id="aff2"></nlm:aff></affiliation></author><author><name sortKey="Moog, Claude H" sort="Moog, Claude H" uniqKey="Moog C" first="Claude H." last="Moog">Claude H. Moog</name><affiliation><nlm:aff id="aff2"></nlm:aff></affiliation></author><author><name sortKey="Stan, Guy Bart" sort="Stan, Guy Bart" uniqKey="Stan G" first="Guy-Bart" last="Stan">Guy-Bart Stan</name><affiliation><nlm:aff id="aff3"></nlm:aff></affiliation></author><author><name sortKey="Brunet, Cecile" sort="Brunet, Cecile" uniqKey="Brunet C" first="Cecile" last="Brunet">Cecile Brunet</name><affiliation><nlm:aff id="aff4"></nlm:aff></affiliation><affiliation><nlm:aff id="aff5"></nlm:aff></affiliation></author><author><name sortKey="Raffi, Francois" sort="Raffi, Francois" uniqKey="Raffi F" first="François" last="Raffi">François Raffi</name><affiliation><nlm:aff id="aff4"></nlm:aff></affiliation><affiliation><nlm:aff id="aff5"></nlm:aff></affiliation></author><author><name sortKey="Ferre, Virginie" sort="Ferre, Virginie" uniqKey="Ferre V" first="Virginie" last="Ferré">Virginie Ferré</name><affiliation><nlm:aff id="aff4"></nlm:aff></affiliation><affiliation><nlm:aff id="aff5"></nlm:aff></affiliation></author><author><name sortKey="Costanza, Vicente" sort="Costanza, Vicente" uniqKey="Costanza V" first="Vicente" last="Costanza">Vicente Costanza</name><affiliation><nlm:aff id="aff1"></nlm:aff></affiliation></author><author><name sortKey="Mhawej, Marie J" sort="Mhawej, Marie J" uniqKey="Mhawej M" first="Marie J." last="Mhawej">Marie J. Mhawej</name><affiliation><nlm:aff id="aff2"></nlm:aff></affiliation></author><author><name sortKey="Biafore, Federico" sort="Biafore, Federico" uniqKey="Biafore F" first="Federico" last="Biafore">Federico Biafore</name><affiliation><nlm:aff id="aff6"></nlm:aff></affiliation></author><author><name sortKey="Ouattara, Djomangan A" sort="Ouattara, Djomangan A" uniqKey="Ouattara D" first="Djomangan A." last="Ouattara">Djomangan A. Ouattara</name><affiliation><nlm:aff id="aff2"></nlm:aff></affiliation></author><author><name sortKey="Ernst, Damien" sort="Ernst, Damien" uniqKey="Ernst D" first="Damien" last="Ernst">Damien Ernst</name><affiliation><nlm:aff id="aff7"></nlm:aff></affiliation></author><author><name sortKey="Fonteneau, Raphael" sort="Fonteneau, Raphael" uniqKey="Fonteneau R" first="Raphael" last="Fonteneau">Raphael Fonteneau</name><affiliation><nlm:aff id="aff7"></nlm:aff></affiliation></author><author><name sortKey="Xia, Xiaohua" sort="Xia, Xiaohua" uniqKey="Xia X" first="Xiaohua" last="Xia">Xiaohua Xia</name><affiliation><nlm:aff id="aff8"></nlm:aff></affiliation></author></analytic><series><title level="j">BioResearch Open Access</title><idno type="ISSN">2164-7844</idno><idno type="eISSN">2164-7860</idno><imprint><date when="2014">2014</date></imprint></series></biblStruct></sourceDesc></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en"><title>Abstract</title><p>This review shows the potential ground-breaking impact that mathematical tools may have in the analysis and the understanding of the HIV dynamics. In the first part, early diagnosis of immunological failure is inferred from the estimation of certain parameters of a mathematical model of the HIV infection dynamics. This method is supported by clinical research results from an original clinical trial: data just after 1 month following therapy initiation are used to carry out the model identification. The diagnosis is shown to be consistent with results from monitoring of the patients after 6 months. In the second part of this review, prospective research results are given for the design of individual anti-HIV treatments optimizing the recovery of the immune system and minimizing side effects. In this respect, two methods are discussed. The first one combines HIV population dynamics with pharmacokinetics and pharmacodynamics models to generate drug treatments using impulsive control systems. The second one is based on optimal control theory and uses a recently published differential equation to model the side effects produced by highly active antiretroviral therapy therapies. The main advantage of these revisited methods is that the drug treatment is computed directly in amounts of drugs, which is easier to interpret by physicians and patients.</p></div></front><back><div1 type="bibliography"><listBibl><biblStruct><analytic><author><name sortKey="Ho, Dd" uniqKey="Ho D">DD Ho</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Perelson, As" uniqKey="Perelson A">AS Perelson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Perelson, As" uniqKey="Perelson A">AS Perelson</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Mhawej, Mj" uniqKey="Mhawej M">MJ Mhawej</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ouattara, Da" uniqKey="Ouattara D">DA Ouattara</name></author></analytic></biblStruct><biblStruct><analytic><author><name sortKey="Ouattara, Da" uniqKey="Ouattara D">DA 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<front><journal-meta><journal-id journal-id-type="nlm-ta">Biores Open Access</journal-id><journal-id journal-id-type="iso-abbrev">Biores Open Access</journal-id><journal-id journal-id-type="publisher-id">biores</journal-id><journal-title-group><journal-title>BioResearch Open Access</journal-title></journal-title-group><issn pub-type="ppub">2164-7844</issn><issn pub-type="epub">2164-7860</issn><publisher><publisher-name>Mary Ann Liebert, Inc.</publisher-name><publisher-loc>140 Huguenot Street, 3rd FloorNew Rochelle, NY 10801USA</publisher-loc></publisher></journal-meta><article-meta><article-id pub-id-type="pmid">25371860</article-id><article-id pub-id-type="pmc">4215334</article-id><article-id pub-id-type="publisher-id">10.1089/biores.2014.0024</article-id><article-id pub-id-type="doi">10.1089/biores.2014.0024</article-id><article-categories><subj-group subj-group-type="heading"><subject>Mini-Review</subject></subj-group></article-categories><title-group><article-title>Mathematical Modeling of HIV Dynamics After Antiretroviral Therapy Initiation: A Review</article-title></title-group><contrib-group><contrib contrib-type="author" corresp="yes"><name><surname>Rivadeneira</surname><given-names>Pablo S.</given-names></name><xref ref-type="aff" rid="aff1"><sup>1,</sup></xref><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Moog</surname><given-names>Claude H.</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Stan</surname><given-names>Guy-Bart</given-names></name><xref ref-type="aff" rid="aff3"><sup>3</sup></xref></contrib><contrib contrib-type="author"><name><surname>Brunet</surname><given-names>Cecile</given-names></name><xref ref-type="aff" rid="aff4"><sup>4,</sup></xref><xref ref-type="aff" rid="aff5"><sup>5</sup></xref></contrib><contrib contrib-type="author"><name><surname>Raffi</surname><given-names>François</given-names></name><xref ref-type="aff" rid="aff4"><sup>4,</sup></xref><xref ref-type="aff" rid="aff5"><sup>5</sup></xref></contrib><contrib contrib-type="author"><name><surname>Ferré</surname><given-names>Virginie</given-names></name><xref ref-type="aff" rid="aff4"><sup>4,</sup></xref><xref ref-type="aff" rid="aff5"><sup>5</sup></xref></contrib><contrib contrib-type="author"><name><surname>Costanza</surname><given-names>Vicente</given-names></name><xref ref-type="aff" rid="aff1"><sup>1</sup></xref></contrib><contrib contrib-type="author"><name><surname>Mhawej</surname><given-names>Marie J.</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Biafore</surname><given-names>Federico</given-names></name><xref ref-type="aff" rid="aff6"><sup>6</sup></xref></contrib><contrib contrib-type="author"><name><surname>Ouattara</surname><given-names>Djomangan A.</given-names></name><xref ref-type="aff" rid="aff2"><sup>2</sup></xref></contrib><contrib contrib-type="author"><name><surname>Ernst</surname><given-names>Damien</given-names></name><xref ref-type="aff" rid="aff7"><sup>7</sup></xref></contrib><contrib contrib-type="author"><name><surname>Fonteneau</surname><given-names>Raphael</given-names></name><xref ref-type="aff" rid="aff7"><sup>7</sup></xref></contrib><contrib contrib-type="author"><name><surname>Xia</surname><given-names>Xiaohua</given-names></name><xref ref-type="aff" rid="aff8"><sup>8</sup></xref></contrib><aff id="aff1"><label><sup>1</sup></label>Nonlinear System Group,<institution>INTEC-Facultad de Ingeniería Química (UNL-CONICET)</institution>, Santa Fe,<country>Argentina</country>.</aff><aff id="aff2"><label><sup>2</sup></label><institution>L'UNAM</institution>, IRCCyN, UMR-CNRS 6597, Nantes,<country>France</country>.</aff><aff id="aff3"><label><sup>3</sup></label>Imperial College London,<institution>Department of Bioengineering</institution>, South Kensington Campus,<country>United Kingdom</country>.</aff><aff id="aff4"><label><sup>4</sup></label>Infectious Diseases,<institution>University Hospital</institution>, Nantes,<country>France</country>.</aff><aff id="aff5"><label><sup>5</sup></label>EA4271 Immunovirologie et polymorphisme génétique,<institution>Nantes University</institution>, Nantes,<country>France</country>.</aff><aff id="aff6"><label><sup>6</sup></label>Center of Applied Mathematics, School of Science and Technology,<institution>National University of San Martin</institution>, San Martín, Buenos Aires,<country>Argentina</country>.</aff><aff id="aff7"><label><sup>7</sup></label><institution>University of Liège</institution>, Department of Electrical Engineering and Computer Science, Montefiore Institute, Liège,<country>Belgium</country>.</aff><aff id="aff8"><label><sup>8</sup></label>Department of Electrical, Electronic and Computer Engineering,<institution>University of Pretoria</institution>, Pretoria,<country>South Africa</country>.</aff></contrib-group><author-notes><corresp><addr-line>Address correspondence to:</addr-line><addr-line><italic>Dr. Pablo S. Rivadeneira</italic></addr-line><addr-line><italic>Nonlinear System Group</italic></addr-line><institution><italic>INTEC – CONICET</italic></institution><addr-line><italic>Güemes 3450, C.P. 3000</italic></addr-line><addr-line><italic>Santa Fe</italic></addr-line><country>Argentina</country><break></break><italic>E-mail:</italic><email xlink:href="mailto:psrivade@santafe-conicet.gov.ar">psrivade@santafe-conicet.gov.ar</email></corresp></author-notes><pub-date pub-type="ppub"><day>01</day><month>10</month><year>2014</year><pmc-comment>string-date: October 2014</pmc-comment>
</pub-date><pub-date pub-type="pmc-release"><day>01</day><month>10</month><year>2014</year><pmc-comment>string-date: October 2014</pmc-comment>
</pub-date><pmc-comment> PMC Release delay is 0 months and 0 days and was based on the
<volume>3</volume><issue>5</issue><fpage>233</fpage><lpage>241</lpage><permissions><copyright-statement>Copyright 2014, Mary Ann Liebert, Inc.</copyright-statement><copyright-year>2014</copyright-year></permissions><self-uri content-type="pdf" xlink:type="simple" xlink:href="biores.2014.0024.pdf"></self-uri><abstract><title>Abstract</title><p>This review shows the potential ground-breaking impact that mathematical tools may have in the analysis and the understanding of the HIV dynamics. In the first part, early diagnosis of immunological failure is inferred from the estimation of certain parameters of a mathematical model of the HIV infection dynamics. This method is supported by clinical research results from an original clinical trial: data just after 1 month following therapy initiation are used to carry out the model identification. The diagnosis is shown to be consistent with results from monitoring of the patients after 6 months. In the second part of this review, prospective research results are given for the design of individual anti-HIV treatments optimizing the recovery of the immune system and minimizing side effects. In this respect, two methods are discussed. The first one combines HIV population dynamics with pharmacokinetics and pharmacodynamics models to generate drug treatments using impulsive control systems. The second one is based on optimal control theory and uses a recently published differential equation to model the side effects produced by highly active antiretroviral therapy therapies. The main advantage of these revisited methods is that the drug treatment is computed directly in amounts of drugs, which is easier to interpret by physicians and patients.</p></abstract><kwd-group kwd-group-type="author"><title><bold>Key words:</bold> </title><kwd>aid for diagnosis</kwd><kwd>AIDS</kwd><kwd>apoptosis</kwd><kwd>dynamical systems</kwd><kwd>HIV</kwd><kwd>modeling</kwd><kwd>nonlinear control</kwd><kwd>pharmacodynamics</kwd><kwd>pharmacokinetics</kwd></kwd-group><counts><fig-count count="5"></fig-count><equation-count count="14"></equation-count><ref-count count="47"></ref-count><page-count count="9"></page-count></counts></article-meta></front></pmc><affiliations><list></list><tree><noCountry><name sortKey="Biafore, Federico" sort="Biafore, Federico" uniqKey="Biafore F" first="Federico" last="Biafore">Federico Biafore</name><name sortKey="Brunet, Cecile" sort="Brunet, Cecile" uniqKey="Brunet C" first="Cecile" last="Brunet">Cecile Brunet</name><name sortKey="Costanza, Vicente" sort="Costanza, Vicente" uniqKey="Costanza V" first="Vicente" last="Costanza">Vicente Costanza</name><name sortKey="Ernst, Damien" sort="Ernst, Damien" uniqKey="Ernst D" first="Damien" last="Ernst">Damien Ernst</name><name sortKey="Ferre, Virginie" sort="Ferre, Virginie" uniqKey="Ferre V" first="Virginie" last="Ferré">Virginie Ferré</name><name sortKey="Fonteneau, Raphael" sort="Fonteneau, Raphael" uniqKey="Fonteneau R" first="Raphael" last="Fonteneau">Raphael Fonteneau</name><name sortKey="Mhawej, Marie J" sort="Mhawej, Marie J" uniqKey="Mhawej M" first="Marie J." last="Mhawej">Marie J. Mhawej</name><name sortKey="Moog, Claude H" sort="Moog, Claude H" uniqKey="Moog C" first="Claude H." last="Moog">Claude H. Moog</name><name sortKey="Ouattara, Djomangan A" sort="Ouattara, Djomangan A" uniqKey="Ouattara D" first="Djomangan A." last="Ouattara">Djomangan A. Ouattara</name><name sortKey="Raffi, Francois" sort="Raffi, Francois" uniqKey="Raffi F" first="François" last="Raffi">François Raffi</name><name sortKey="Rivadeneira, Pablo S" sort="Rivadeneira, Pablo S" uniqKey="Rivadeneira P" first="Pablo S." last="Rivadeneira">Pablo S. Rivadeneira</name><name sortKey="Stan, Guy Bart" sort="Stan, Guy Bart" uniqKey="Stan G" first="Guy-Bart" last="Stan">Guy-Bart Stan</name><name sortKey="Xia, Xiaohua" sort="Xia, Xiaohua" uniqKey="Xia X" first="Xiaohua" last="Xia">Xiaohua Xia</name></noCountry></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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