- Author:
- Tommy Yu <tommy.yu@auckland.ac.nz>
- Date:
- 2010-08-25 18:51:43+12:00
- Desc:
- xml:base fix
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/wodarz_nowak_1999/rawfile/9b46e976aaadd1c0a5ff7ac11489f7e99d8dbbe7/wodarz_nowak_1999.cellml
<?xml version="1.0" encoding="utf-8"?>
<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" cmeta:id="wodarz_1999" name="wodarz_1999">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Specific therapy regimes could lead to long-term immunological control of HIV</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This CellML model runs in OpenCell to replicate the graphs in Figure 1 (i) and (ii) in the original paper. The units have been checked and they are consistent. The CellML model also runs in COR, but due time being expressed in days, the model is not really suitable for simulation in COR (where time is expressed in milliseconds).
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: We use mathematical models to study the relationship between HIV and the immune system during the natural course of infection and in the context of different antiviral treatment regimes. The models suggest that an efficient cytotoxic T lymphocyte (CTL) memory response is required to control the virus. We define CTL memory as long-term persistence of CTL precursors in the absence of antigen. Infection and depletion of CD4(+) T helper cells interfere with CTL memory generation, resulting in persistent viral replication and disease progression. We find that antiviral drug therapy during primary infection can enable the development of CTL memory. In chronically infected patients, specific treatment schedules, either including deliberate drug holidays or antigenic boosts of the immune system, can lead to a re-establishment of CTL memory. Whether such treatment regimes would lead to long-term immunologic control deserves investigation under carefully controlled conditions.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Specific therapy regimes could lead to long-term immunological control of HIV, Dominik Wodarz and Martin A. Nowak, 1999,<emphasis>Proceedings of the National Academy of Sciences, USA</emphasis>, 96, 14464-14469. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/10588728">PubMed ID: 10588728</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram</title>
</objectinfo>
<imagedata fileref="wodarz_1999.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of a model of the interaction between HIV and the immune system.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<units name="mm3">
<unit exponent="3" prefix="milli" units="metre"/>
</units>
<units name="per_mm3">
<unit exponent="-1" units="mm3"/>
</units>
<units name="hour">
<unit multiplier="3600" units="second"/>
</units>
<units name="day">
<unit multiplier="86400" units="second"/>
</units>
<units name="per_day">
<unit exponent="-1" units="day"/>
</units>
<units name="per_mm3_per_day">
<unit units="per_mm3"/>
<unit exponent="-1" units="day"/>
</units>
<units name="mm3_per_day">
<unit units="mm3"/>
<unit exponent="-1" units="day"/>
</units>
<units name="mm3_mm3_per_day">
<unit units="mm3"/>
<unit units="mm3"/>
<unit exponent="-1" units="day"/>
</units>
<component name="environment">
<variable cmeta:id="environment_time" name="time" public_interface="out" units="day"/>
</component>
<component name="x">
<variable cmeta:id="x_x" initial_value="10" name="x" public_interface="out" units="per_mm3"/>
<variable initial_value="1" name="lamda" units="per_mm3_per_day"/>
<variable initial_value="0.1" name="d" units="per_day"/>
<variable name="beta" public_interface="in" units="mm3_per_day"/>
<variable name="s" public_interface="in" units="dimensionless"/>
<variable name="y" public_interface="in" units="per_mm3"/>
<variable name="time" public_interface="in" units="day"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>x</ci>
</apply>
<apply>
<minus/>
<ci>lamda</ci>
<apply>
<plus/>
<apply>
<times/>
<ci>d</ci>
<ci>x</ci>
</apply>
<apply>
<times/>
<ci>s</ci>
<ci>beta</ci>
<ci>x</ci>
<ci>y</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="y">
<variable cmeta:id="y_y" initial_value="0.1" name="y" public_interface="out" units="per_mm3"/>
<variable initial_value="0.2" name="a" units="per_day"/>
<variable name="p" public_interface="in" units="mm3_per_day"/>
<variable name="beta" public_interface="in" units="mm3_per_day"/>
<variable name="s" public_interface="in" units="dimensionless"/>
<variable name="x" public_interface="in" units="per_mm3"/>
<variable name="z" public_interface="in" units="per_mm3"/>
<variable name="time" public_interface="in" units="day"/>
<variable cmeta:id="y_log_y" name="log_y" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>y</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>s</ci>
<ci>beta</ci>
<ci>x</ci>
<ci>y</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>a</ci>
<ci>y</ci>
</apply>
<apply>
<times/>
<ci>p</ci>
<ci>y</ci>
<ci>z</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>log_y</ci>
<apply>
<log/>
<apply>
<times/>
<ci>y</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mm3">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="w">
<variable cmeta:id="w_w" initial_value="0.001" name="w" public_interface="out" units="per_mm3"/>
<variable initial_value="0.01" name="b" units="per_day"/>
<variable name="c" public_interface="in" units="mm3_mm3_per_day"/>
<variable name="q" public_interface="in" units="per_mm3"/>
<variable name="x" public_interface="in" units="per_mm3"/>
<variable name="y" public_interface="in" units="per_mm3"/>
<variable name="time" public_interface="in" units="day"/>
<variable cmeta:id="w_log_w" name="log_w" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>w</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>c</ci>
<ci>x</ci>
<ci>y</ci>
<ci>w</ci>
</apply>
<apply>
<plus/>
<apply>
<times/>
<ci>c</ci>
<ci>q</ci>
<ci>y</ci>
<ci>w</ci>
</apply>
<apply>
<times/>
<ci>b</ci>
<ci>w</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>log_w</ci>
<apply>
<log/>
<apply>
<times/>
<ci>w</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="mm3">1</cn>
</apply>
</apply>
</apply>
</math>
</component>
<component name="z">
<variable cmeta:id="z_z" initial_value="0" name="z" public_interface="out" units="per_mm3"/>
<variable initial_value="0.1" name="h" units="per_day"/>
<variable name="c" public_interface="in" units="mm3_mm3_per_day"/>
<variable name="q" public_interface="in" units="per_mm3"/>
<variable name="y" public_interface="in" units="per_mm3"/>
<variable name="w" public_interface="in" units="per_mm3"/>
<variable name="time" public_interface="in" units="day"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>z</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>c</ci>
<ci>q</ci>
<ci>y</ci>
<ci>w</ci>
</apply>
<apply>
<times/>
<ci>h</ci>
<ci>z</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="kinetic_parameters">
<variable initial_value="0.5" name="beta" public_interface="out" units="mm3_per_day"/>
<variable initial_value="1" name="p" public_interface="out" units="mm3_per_day"/>
<variable initial_value="0.5" name="q" public_interface="out" units="per_mm3"/>
<variable initial_value="0.1" name="c" public_interface="out" units="mm3_mm3_per_day"/>
<variable name="s" public_interface="out" units="dimensionless"/>
<variable name="time" public_interface="in" units="day"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>s</ci>
<piecewise>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<leq/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="day">15</cn>
</apply>
</piece>
<piece>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<geq/>
<ci>time</ci>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="day">40</cn>
</apply>
</piece>
<otherwise>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">0.0042</cn>
</otherwise>
</piecewise>
</apply>
</math>
</component>
<connection>
<map_components component_1="x" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="y" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="w" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="z" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="kinetic_parameters" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="w" component_2="y"/>
<map_variables variable_1="y" variable_2="y"/>
</connection>
<connection>
<map_components component_1="w" component_2="z"/>
<map_variables variable_1="w" variable_2="w"/>
</connection>
<connection>
<map_components component_1="w" component_2="x"/>
<map_variables variable_1="x" variable_2="x"/>
</connection>
<connection>
<map_components component_1="y" component_2="x"/>
<map_variables variable_1="x" variable_2="x"/>
<map_variables variable_1="y" variable_2="y"/>
</connection>
<connection>
<map_components component_1="y" component_2="z"/>
<map_variables variable_1="z" variable_2="z"/>
<map_variables variable_1="y" variable_2="y"/>
</connection>
<connection>
<map_components component_1="x" component_2="kinetic_parameters"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="s" variable_2="s"/>
</connection>
<connection>
<map_components component_1="y" component_2="kinetic_parameters"/>
<map_variables variable_1="beta" variable_2="beta"/>
<map_variables variable_1="p" variable_2="p"/>
<map_variables variable_1="s" variable_2="s"/>
</connection>
<connection>
<map_components component_1="w" component_2="kinetic_parameters"/>
<map_variables variable_1="c" variable_2="c"/>
<map_variables variable_1="q" variable_2="q"/>
</connection>
<connection>
<map_components component_1="z" component_2="kinetic_parameters"/>
<map_variables variable_1="c" variable_2="c"/>
<map_variables variable_1="q" variable_2="q"/>
</connection>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:about="rdf:#af447236-dafc-4946-8114-3b5052d5a1d0"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
Proceedings of the National Academy of Science, USA
</title></rdf:Description><rdf:Description rdf:about="rdf:#8abdb10e-b3ed-44be-a05a-ce615ea4545c"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#60399e65-0d79-4825-a043-47226f0c3fe2"/></N><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type></rdf:Description><rdf:Description rdf:about="#x"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">x</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">uninfected CD4 T cells</alternative></rdf:Description><rdf:Description rdf:about="rdf:#87139b86-0c59-45f0-b9b6-39664789dc6c"><subject_type xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">keyword</subject_type><rdf:value><rdf:Description rdf:about="rdf:#e7d0d0ba-44bb-4c3e-85fc-5e16b5ff914a"/></rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#4bec66e7-25cf-4d6e-a052-027da9d50d73"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">A</Other><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Nowak</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Martin</Given></rdf:Description><rdf:Description rdf:about="#w"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">w</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">cytotoxic T lymphocyte precursors</alternative></rdf:Description><rdf:Description rdf:about="rdf:#a5304b8d-9b2b-4fe0-acdd-1639e7983c10"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2003-12-10</W3CDTF></rdf:Description><rdf:Description rdf:about="rdf:#60399e65-0d79-4825-a043-47226f0c3fe2"><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Wodarz</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Dominik</Given></rdf:Description><rdf:Description rdf:about="#z"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">z</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">CTL effectors</alternative></rdf:Description><rdf:Description rdf:about="rdf:#89e40e51-31a3-41ba-9ff1-e308a5495fca"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">1999-12-07</W3CDTF></rdf:Description><rdf:Description rdf:about="rdf:#d4b8ea64-6ef1-423d-8b71-c2ac37847b51"><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">10588728</Pubmed_id><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#f6107ea5-aeb6-4eb9-b355-ad5a2b00dc5b"/></JournalArticle></rdf:Description><rdf:Description rdf:nodeID="n1"><rdf:rest><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/></rdf:rest><rdf:first><rdf:Description rdf:nodeID="n2"/></rdf:first></rdf:Description><rdf:Description rdf:about="rdf:#e7d0d0ba-44bb-4c3e-85fc-5e16b5ff914a"><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/></rdf:type><rdf:_4 xml:lang="en">pharmacology</rdf:_4><rdf:_3 xml:lang="en">immunology</rdf:_3><rdf:_2 xml:lang="en">hiv-1</rdf:_2><rdf:_1 xml:lang="en">viral dynamics</rdf:_1></rdf:Description><rdf:Description rdf:about="rdf:#1df4bf08-d084-4e49-acca-425082f281e4"><rdf:type><rdf:Description rdf:about="http://imc.org/vCard/3.0#internet"/></rdf:type><rdf:value xml:lang="en">c.lloyd@auckland.ac.nz</rdf:value></rdf:Description><rdf:Description rdf:nodeID="n2"><endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">300</endingValue></rdf:Description><rdf:Description rdf:about="rdf:#26a3786b-dd55-4869-8004-8eed55f2639c"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">May</Other><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Lloyd</Family><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine</Given></rdf:Description><rdf:Description rdf:about="rdf:#a6357a12-e3a9-4cb1-99f0-d1c458f3de6d"><Orgname xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">The University of Auckland</Orgname><Orgunit xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Auckland Bioengineering Institute</Orgunit></rdf:Description><rdf:Description rdf:about="rdf:#21670d63-64d5-47a8-a297-86784af7b779"><rdf:value xml:lang="en">
This is the CellML description of Wodarz and Nowak's 1999 mathematical model of immunological control of HIV.
</rdf:value><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#0fe62888-2090-455c-8e2c-de0c0a7e55e7"/></creator></rdf:Description><rdf:Description rdf:about=""><publisher xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
The University of Auckland, Bioengineering Institute
</publisher><created xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#a5304b8d-9b2b-4fe0-acdd-1639e7983c10"/></created><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#db6e062c-563e-407f-a1d2-c450585f1520"/></creator></rdf:Description><rdf:Description rdf:about="rdf:#6c7a081e-791f-4fcf-9f38-d85939718ce3"><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Seq"/></rdf:type><rdf:_2><rdf:Description rdf:about="rdf:#2ab13ece-c44d-44b0-8726-6ec05d7cc973"/></rdf:_2><rdf:_1><rdf:Description rdf:about="rdf:#8abdb10e-b3ed-44be-a05a-ce615ea4545c"/></rdf:_1></rdf:Description><rdf:Description rdf:about="rdf:#a79966ef-e84e-4c3c-8136-9616ce6804c2"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#87139b86-0c59-45f0-b9b6-39664789dc6c"/></subject></rdf:Description><rdf:Description rdf:about="rdf:#f6107ea5-aeb6-4eb9-b355-ad5a2b00dc5b"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
Specific therapy regimes could lead to long-term immunological
control of HIV
</title><first_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">14464</first_page><volume xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">96</volume><last_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">14469</last_page><issued xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#89e40e51-31a3-41ba-9ff1-e308a5495fca"/></issued><Journal xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#af447236-dafc-4946-8114-3b5052d5a1d0"/></Journal><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#6c7a081e-791f-4fcf-9f38-d85939718ce3"/></creator></rdf:Description><rdf:Description rdf:about="#y"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">y</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">infected CD4 T cells</alternative></rdf:Description><rdf:Description rdf:nodeID="n3"><boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n1"/></boundIntervals></rdf:Description><rdf:Description rdf:about="#wodarz_1999"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
Wodarz and Nowak's 1999 mathematical model of immunological control of
HIV.
</title><simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#"><rdf:Description rdf:nodeID="n3"/></simulation><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#a79966ef-e84e-4c3c-8136-9616ce6804c2"/></reference><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#d4b8ea64-6ef1-423d-8b71-c2ac37847b51"/></reference><cmeta:comment><rdf:Description rdf:about="rdf:#21670d63-64d5-47a8-a297-86784af7b779"/></cmeta:comment></rdf:Description><rdf:Description rdf:about="rdf:#0fe62888-2090-455c-8e2c-de0c0a7e55e7"><FN xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine Lloyd</FN></rdf:Description><rdf:Description rdf:about="rdf:#db6e062c-563e-407f-a1d2-c450585f1520"><EMAIL xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#1df4bf08-d084-4e49-acca-425082f281e4"/></EMAIL><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#26a3786b-dd55-4869-8004-8eed55f2639c"/></N><ORG xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#a6357a12-e3a9-4cb1-99f0-d1c458f3de6d"/></ORG></rdf:Description><rdf:Description rdf:about="rdf:#2ab13ece-c44d-44b0-8726-6ec05d7cc973"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#4bec66e7-25cf-4d6e-a052-027da9d50d73"/></N><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type></rdf:Description></rdf:RDF></model>
