- Author:
- pmr2.import <nobody@models.cellml.org>
- Date:
- 2009-06-17 15:17:06+12:00
- Desc:
- committing version01 of nelson_murray_perelson_2000
- Permanent Source URI:
- https://models.physiomeproject.org/workspace/nelson_murray_perelson_2000/rawfile/72977575e7090da8bba2a30e080d5c645f374212/nelson_murray_perelson_2000.cellml
<?xml version='1.0' encoding='utf-8'?>
<!-- FILE : nelson_model_2000.xml
CREATED : 5th December 2002
LAST MODIFIED : 20th April 2005
AUTHOR : Catherine Lloyd
Bioengineering Institute
The University of Auckland
MODEL STATUS : This model conforms to the CellML 1.0 Specification released on
10th August 2001, and the 16/01/2002 CellML Metadata 1.0 Specification.
DESCRIPTION : This file contains a CellML description of Nelson et al's 2000 mathematical model of HIV-1 pathogenesis.
CHANGES:
09/04/2003 - AAC - Added publication date information.
20/04/2005 - PJV - Corrected syntax error with base_units
--><model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" cmeta:id="nelson_murray_perelson_2000_version01" name="nelson_murray_perelson_2000_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>A Model of HIV-1 Pathogenesis</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This is the original unchecked version of the model imported from the previous
CellML model repository, 24-Jan-2006.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
In recent years, clinical research together with mathematical modelling has enhanced our understanding of HIV-1 infection dynamics. For example, the introduction of a new class of antiretroviral drugs called protease inhibitors has helped to define the kinetic parameters underlying HIV-1 infection. However, many of the mathematical models that have been developed have incorrectly assumed that drug treatments are 100 percent effective, and that upon infection, a cell immediately begins to produce virus.
</para>
<para>
In HIV-1 infection, the virus life cycle plays a crucial role in disease progression. The binding of a viral particle to a receptor on a target T-cell initiates a cascade of of events that can lead to the targeted cell becoming productively infected, that is, producing new virus (see <xref linkend="fig_reaction_diagram"/> below). There is a significant time delay between initial viral entry into a cell and subsequent viral production.
</para>
<para>
In 2000, Nelson <emphasis>et al.</emphasis> published a mathematical model of HIV-1 pathogenesis that included an intracellular delay in the initiation of virus production. Their model also allowed for the fact that the effects of drugs can be less than perfect. Analysis showed that when drug efficacy is less than perfect, as is frequently the case <emphasis>in vivo</emphasis>, the predicted rate of decline in plasma virus concentration depends on three factors: the death rate of infected, virus producing T-cells, the efficacy of the drug therapy, and the length of the time delay between infection of a T-cell and virus production. From their model, Nelson <emphasis>et al.</emphasis> suggest that previous estimates of infected cell loss rates may be unrealistic and could be improved upon by considering more realistic models of viral infection.
</para>
<para>
The complete original paper reference is cited below:
</para>
<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VHX-3YJ9XCP-4&_coverDate=02%2F29%2F2000&_alid=68316140&_rdoc=1&_fmt=&_orig=search&_qd=1&_cdi=6078&_sort=d&wchp=dGLbVzz-lSztz&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=35355b0a01982e7e3335290b4c3f850c">A model of HIV-1 pathogenesis that includes an intracellular delay</ulink>, Patrick W. Nelson, James D. Murray, and Alan S. Perelson, 2000, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&_cdi=6078&_auth=y&_acct=C000011498&_version=1&_urlVersion=0&_userid=140507&md5=fed5116015c6d8a21af255eb3e4d8be9">
<emphasis>Mathematical Biosciences</emphasis>
</ulink>, 163, 201-215. (A PDF version of the article is available for Journal Members on the Mathematical Biosciences journal website.) <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&list_uids=10701304&dopt=Abstract">PubMed ID: 10701304</ulink>
</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>reaction schematic for the model</title>
</objectinfo>
<imagedata fileref="nelson_2000.png"/>
</imageobject>
</mediaobject>
<caption>A schematic diagram showing the cascade of events triggered by the binding of a HIV-1 virus particle to a receptor on a target T-cell.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!--
Below, are defined some additional units for association with variables and
constants within the model.
-->
<units name="day">
<unit units="second" multiplier="86400"/>
</units>
<units base_units="yes" name="cell"/>
<units base_units="yes" name="viron"/>
<units name="cells_per_day">
<unit units="cell"/>
<unit units="day" exponent="-1"/>
</units>
<units name="virons_per_day">
<unit units="viron"/>
<unit units="day" exponent="-1"/>
</units>
<units name="ml">
<unit units="litre" prefix="milli"/>
</units>
<units name="ml_per_virons_per_day">
<unit units="ml"/>
<unit units="viron" exponent="-1"/>
<unit units="day" exponent="-1"/>
</units>
<units name="virons_per_cell">
<unit units="viron"/>
<unit units="cell" exponent="-1"/>
</units>
<units name="virons_per_ml">
<unit units="viron"/>
<unit units="ml" exponent="-1"/>
</units>
<units name="mm3">
<unit units="metre" prefix="milli" exponent="3"/>
</units>
<units name="cells_per_mm3">
<unit units="cell"/>
<unit units="mm3" exponent="-1"/>
</units>
<component name="environment">
<variable units="day" public_interface="out" name="time"/>
<variable units="cells_per_day" public_interface="out" name="delta" initial_value="0.5"/>
<variable units="dimensionless" public_interface="out" name="np" initial_value="1.0"/>
<variable units="virons_per_day" public_interface="out" name="c" initial_value="3.0"/>
<variable units="ml_per_virons_per_day" public_interface="out" name="k" initial_value="3.43E-5"/>
<variable units="virons_per_cell" public_interface="out" name="N" initial_value="480.0"/>
</component>
<component name="uninfected_T_cells">
<variable units="cells_per_mm3" public_interface="out" name="T" initial_value="180.0"/>
</component>
<component name="infected_T_cells">
<variable units="cells_per_mm3" public_interface="out" name="T_in"/>
<variable units="dimensionless" name="m"/>
<variable units="day" name="tau"/>
<variable units="cells_per_day" public_interface="in" name="delta"/>
<variable units="day" public_interface="in" name="time"/>
<variable units="virons_per_ml" public_interface="in" name="VI"/>
<variable units="ml_per_virons_per_day" public_interface="in" name="k"/>
<variable units="cells_per_mm3" public_interface="in" name="T"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="T_in_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> T_in </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> k </ci>
<ci> VI </ci>
<ci> T </ci>
<apply>
<minus/>
<ci> time </ci>
<ci> tau </ci>
</apply>
<apply>
<exp/>
<apply>
<times/>
<apply>
<minus/>
<ci> m </ci>
</apply>
<ci> tau </ci>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci> delta </ci>
<ci> T_in </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="infectious_virus">
<variable units="virons_per_ml" public_interface="out" name="VI"/>
<variable units="cells_per_day" public_interface="in" name="delta"/>
<variable units="day" public_interface="in" name="time"/>
<variable units="virons_per_cell" public_interface="in" name="N"/>
<variable units="dimensionless" public_interface="in" name="np"/>
<variable units="virons_per_day" public_interface="in" name="c"/>
<variable units="cells_per_mm3" public_interface="in" name="T_in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="VI_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> VI </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<apply>
<minus/>
<cn cellml:units="dimensionless"> 1.0 </cn>
<ci> np </ci>
</apply>
<ci> N </ci>
<ci> delta </ci>
<ci> T_in </ci>
</apply>
<apply>
<times/>
<ci> c </ci>
<ci> VI </ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="non_infectious_virus">
<variable units="virons_per_ml" public_interface="out" name="VNI"/>
<variable units="cells_per_day" public_interface="in" name="delta"/>
<variable units="day" public_interface="in" name="time"/>
<variable units="virons_per_cell" public_interface="in" name="N"/>
<variable units="dimensionless" public_interface="in" name="np"/>
<variable units="virons_per_day" public_interface="in" name="c"/>
<variable units="cells_per_mm3" public_interface="in" name="T_in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply id="VNI_diff_eq">
<eq/>
<apply>
<diff/>
<bvar>
<ci> time </ci>
</bvar>
<ci> VNI </ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci> np </ci>
<ci> N </ci>
<ci> delta </ci>
<ci> T_in </ci>
</apply>
<apply>
<times/>
<ci> c </ci>
<ci> VNI </ci>
</apply>
</apply>
</apply>
</math>
</component>
<group>
<relationship_ref relationship="containment"/>
<component_ref component="environment">
<component_ref component="uninfected_T_cells"/>
<component_ref component="infected_T_cells"/>
<component_ref component="infectious_virus"/>
<component_ref component="non_infectious_virus"/>
</component_ref>
</group>
<connection>
<map_components component_2="environment" component_1="infected_T_cells"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="k" variable_1="k"/>
<map_variables variable_2="delta" variable_1="delta"/>
</connection>
<connection>
<map_components component_2="environment" component_1="infectious_virus"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="np" variable_1="np"/>
<map_variables variable_2="N" variable_1="N"/>
<map_variables variable_2="c" variable_1="c"/>
<map_variables variable_2="delta" variable_1="delta"/>
</connection>
<connection>
<map_components component_2="environment" component_1="non_infectious_virus"/>
<map_variables variable_2="time" variable_1="time"/>
<map_variables variable_2="np" variable_1="np"/>
<map_variables variable_2="N" variable_1="N"/>
<map_variables variable_2="c" variable_1="c"/>
<map_variables variable_2="delta" variable_1="delta"/>
</connection>
<connection>
<map_components component_2="infected_T_cells" component_1="uninfected_T_cells"/>
<map_variables variable_2="T" variable_1="T"/>
</connection>
<connection>
<map_components component_2="infectious_virus" component_1="infected_T_cells"/>
<map_variables variable_2="T_in" variable_1="T_in"/>
<map_variables variable_2="VI" variable_1="VI"/>
</connection>
<connection>
<map_components component_2="non_infectious_virus" component_1="infected_T_cells"/>
<map_variables variable_2="T_in" variable_1="T_in"/>
</connection>
<rdf:RDF>
<rdf:Bag rdf:about="rdf:#749d1119-0fcc-4a2a-8adc-9827b7083403">
<rdf:li>viral dynamics</rdf:li>
<rdf:li>hiv-1</rdf:li>
<rdf:li>immunology</rdf:li>
</rdf:Bag>
<rdf:Seq rdf:about="rdf:#7a8ec4ac-cc9d-4ecd-84ee-55e4fb2aa8f9">
<rdf:li rdf:resource="rdf:#f30f8234-9eff-4782-bc29-66b4ff442f15"/>
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<rdf:li rdf:resource="rdf:#a69705df-52c6-462b-9ceb-8bfc2bd5fa28"/>
</rdf:Seq>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
<cmeta:modification rdf:resource="rdf:#3978135f-92f8-4c74-96eb-9dcd1f89376e"/>
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<rdf:value>
This is the CellML description of Nelson et al's 2000 mathematical
model of HIV-1 pathogenesis.
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="rdf:#2e7a36f4-a80f-4484-a183-7425f2f1499c">
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<vCard:Given>Autumn</vCard:Given>
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<vCard:Other>A</vCard:Other>
</rdf:Description>
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<vCard:Given>Peter</vCard:Given>
<vCard:Family>Villiger</vCard:Family>
<vCard:Other>J</vCard:Other>
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</rdf:Description>
<rdf:Description rdf:about="rdf:#1718289f-4a02-443a-804d-35c1ed924d4e">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
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<bqs:subject_type>keyword</bqs:subject_type>
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<rdf:Description rdf:about="rdf:#32879fab-cd44-48bd-bc7a-2a3747b8fe0d">
<vCard:Given>James</vCard:Given>
<vCard:Family>Murray</vCard:Family>
<vCard:Other>D</vCard:Other>
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Added publication date information.
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<vCard:Given>Patrick</vCard:Given>
<vCard:Family>Nelson</vCard:Family>
<vCard:Other>W</vCard:Other>
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<dcterms:W3CDTF>2003-04-09</dcterms:W3CDTF>
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<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
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<dc:title>
Nelson et al's 2000 mathematical model of HIV-1 pathogenesis.
</dc:title>
<cmeta:bio_entity>T-cells</cmeta:bio_entity>
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<dc:title>
A model of HIV-1 pathogenesis that includes an intracellular delay
</dc:title>
<bqs:volume>163</bqs:volume>
<bqs:first_page>201</bqs:first_page>
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<rdf:value>
Corrected syntax error with base_units
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<vCard:FN>Catherine Lloyd</vCard:FN>
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<vCard:Given>Alan</vCard:Given>
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<vCard:Other>S</vCard:Other>
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<dcterms:W3CDTF>2005-04-20</dcterms:W3CDTF>
</rdf:Description>
</rdf:RDF>
</model>
