Rendering of the source text

<?xml version="1.0"?>
<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="wodarz_2007" name="wodarz_2007">

<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Infection dynamics in HIV-specific CD4 T cells: Does a CD4 T cell boost benefit the host or the virus?</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 is known to run in both PCEnv and COR to recreate the published results. The units have been checked and they are consistent. The published paper contains four different mathematical models. This particular CellML model represents the second model - which includes a description of the infectious spread of the virus amongst CD4+ T cells.
          </para>
  </section>
  <sect1 id="sec_structure">
  <title>Model Structure</title>

<para>
ABSTRACT: Recent experimental data have shown that HIV-specific CD4 T cells provide a very important target for HIV replication. We use mathematical models to explore the effect of specific CD4 T cell infection on the dynamics of virus spread and immune responses. Infected CD4 T cells can provide antigen for their own stimulation. We show that such autocatalytic cell division can significantly enhance virus spread, and can also provide an additional reservoir for virus persistence during anti-viral drug therapy. In addition, the initial number of HIV-specific CD4 T cells is an important determinant of acute infection dynamics. A high initial number of HIV-specific CD4 T cells can lead to a sudden and fast drop of the population of HIV-specific CD4 T cells which results quickly in their extinction. On the other hand, a low initial number of HIV-specific CD4 T cells can lead to a prolonged persistence of HIV-specific CD4 T cell help at higher levels. The model suggests that boosting the population of HIV-specific CD4 T cells can increase the amount of virus-induced immune impairment, lead to less efficient anti-viral effector responses, and thus speed up disease progression, especially if effector responses such as CTL have not been sufficiently boosted at the same time.
</para>

<para>
The original paper reference is cited below:
</para>

<para>
Infection dynamics in HIV-specific CD4 T cells: Does a CD4 T cell boost benefit the host or the virus?, Dominik Wodarz and Dean H. Hamer, 2007, <emphasis>Mathematical Biosciences</emphasis> <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/17379260">PubMed ID: 17379260</ulink>
</para>

<informalfigure float="0" id="fig_diagram">
<mediaobject>
  <imageobject>
    <imagedata fileref="wodarz_2007b.png"/>
  </imageobject>
</mediaobject>
<caption>A schematic diagram describing the mathematical model.</caption>
</informalfigure>

</sect1>
</article>
</documentation> 


  
  <units name="first_order_rate_constant">
    <unit exponent="-1" units="second"/>
  </units>
  
  <component name="environment">
    <variable cmeta:id="environment_time" name="time" public_interface="out" units="second"/>
  </component>

  <component cmeta:id="x" name="x">
      
    <variable cmeta:id="x_x" initial_value="0.1" name="x" public_interface="out" units="dimensionless"/>

    <variable name="r" public_interface="in" units="first_order_rate_constant"/>
    <variable name="v" public_interface="in" units="dimensionless"/>
    <variable name="y" public_interface="in" units="dimensionless"/>
    <variable name="k" public_interface="in" units="dimensionless"/>
    <variable name="d" public_interface="in" units="first_order_rate_constant"/>
    <variable name="beta" public_interface="in" units="first_order_rate_constant"/>
    <variable name="time" public_interface="in" units="second"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> x </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> r </ci> 
            <ci> x </ci>
            <ci> v </ci>
            <apply>
              <minus/>
              <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
              <apply>
                <divide/>
                <apply>
                  <plus/>
                  <ci> x </ci>
                  <ci> y </ci>
                </apply>
                <ci> k </ci>
              </apply>
            </apply>
          </apply>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> d </ci> 
              <ci> x </ci>
            </apply>
            <apply>
              <times/>
              <ci> beta </ci> 
              <ci> x </ci>
              <ci> v </ci>
            </apply>
          </apply> 
        </apply>
      </apply>    
    </math>
  </component>

  <component cmeta:id="y" name="y">
      
    <variable cmeta:id="y_y" initial_value="0.0" name="y" public_interface="out" units="dimensionless"/>

    <variable name="r" public_interface="in" units="first_order_rate_constant"/>
    <variable name="v" public_interface="in" units="dimensionless"/>
    <variable name="x" public_interface="in" units="dimensionless"/>
    <variable name="k" public_interface="in" units="dimensionless"/>
    <variable name="a" public_interface="in" units="first_order_rate_constant"/>
    <variable name="beta" public_interface="in" units="first_order_rate_constant"/>
    <variable name="time" public_interface="in" units="second"/>
    
    <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>
            <plus/>
            <apply>
              <times/>
              <ci> beta </ci> 
              <ci> x </ci>
              <ci> v </ci>
            </apply>
            <apply>
              <times/>
              <ci> r </ci> 
              <ci> y </ci>
              <ci> v </ci>
              <apply>
                <minus/>
                <cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless"> 1.0 </cn>
                <apply>
                  <divide/>
                  <apply>
                    <plus/>
                    <ci> x </ci>
                    <ci> y </ci>
                  </apply>
                  <ci> k </ci>
                </apply>
              </apply>
            </apply>
          </apply>
          <apply>
            <times/>
            <ci> a </ci> 
            <ci> y </ci>
          </apply> 
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="v" name="v">
      
    <variable cmeta:id="v_v" initial_value="1.0" name="v" public_interface="out" units="dimensionless"/>
    
    <variable name="u" public_interface="in" units="first_order_rate_constant"/>
    <variable name="eta" public_interface="in" units="first_order_rate_constant"/>
    <variable name="y" public_interface="in" units="dimensionless"/>
    <variable name="time" public_interface="in" units="second"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci> v </ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> eta </ci>
            <ci> y </ci>
          </apply>
          <apply>
            <times/>
            <ci> u </ci>
            <ci> v </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>

  <component name="model_parameters"> 
    <variable initial_value="1.0" name="r" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="10.0" name="k" public_interface="out" units="dimensionless"/>
    <variable initial_value="0.1" name="d" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.2" name="beta" public_interface="out" units="first_order_rate_constant"/>
    <variable cmeta:id="model_parameters_a" initial_value="0.2" name="a" public_interface="out" units="first_order_rate_constant"/> 
    <variable initial_value="1.0" name="eta" public_interface="out" units="first_order_rate_constant"/>
    <variable initial_value="0.5" name="u" public_interface="out" units="first_order_rate_constant"/>
  </component>
  
  <connection>
    <map_components component_1="x" component_2="environment"/>
    <map_variables variable_1="time" variable_2="time"/>
  </connection>

  <connection>
    <map_components component_1="v" 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="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="x" component_2="v"/>
    <map_variables variable_1="v" variable_2="v"/>
  </connection>

  <connection>
    <map_components component_1="x" component_2="model_parameters"/>
    <map_variables variable_1="r" variable_2="r"/>
    <map_variables variable_1="k" variable_2="k"/>
    <map_variables variable_1="d" variable_2="d"/>
    <map_variables variable_1="beta" variable_2="beta"/>
  </connection>

  <connection>
    <map_components component_1="y" component_2="v"/>
    <map_variables variable_1="v" variable_2="v"/>
    <map_variables variable_1="y" variable_2="y"/>
  </connection>

  <connection>
    <map_components component_1="y" component_2="model_parameters"/>
    <map_variables variable_1="r" variable_2="r"/>
    <map_variables variable_1="k" variable_2="k"/>
    <map_variables variable_1="a" variable_2="a"/>
    <map_variables variable_1="beta" variable_2="beta"/>
  </connection>

  <connection>
    <map_components component_1="v" component_2="model_parameters"/>
    <map_variables variable_1="eta" variable_2="eta"/>
    <map_variables variable_1="u" variable_2="u"/>
  </connection>
  

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"><rdf:Description rdf:about="rdf:#39074383-8c28-403d-bb59-dac4c5fd9380"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Mathematical Biosciences</title></rdf:Description><rdf:Description rdf:about="rdf:#1a767be3-643c-486c-811f-4dcb1e8723c9"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2007-02</W3CDTF></rdf:Description><rdf:Description rdf:about="rdf:#160a60fc-7260-4c13-a11c-7f055d412a6e"><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#4b4520ce-8e7d-4729-83ab-fbc1da78dcdc"/></N></rdf:Description><rdf:Description rdf:about="rdf:#26118a9d-6018-4598-855d-10953ac95edd"><JournalArticle xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#29f4a722-a049-48b6-a29a-b607763b02b7"/></JournalArticle><Pubmed_id xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">17379260</Pubmed_id></rdf:Description><rdf:Description rdf:about="rdf:#29f4a722-a049-48b6-a29a-b607763b02b7"><Journal xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#39074383-8c28-403d-bb59-dac4c5fd9380"/></Journal><issued xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#1a767be3-643c-486c-811f-4dcb1e8723c9"/></issued><last_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en"/><first_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en"/><volume xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en"/><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#633015ce-17da-408e-9d22-4040b92dc853"/></creator><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Infection dynamics in HIV-specific CD4 T cells: Does a CD4 T cell boost benefit the host or the virus?</title></rdf:Description><rdf:Description rdf:about="rdf:#665b4094-dc8e-4545-babd-39d7d81cf26b"><rdf:value xml:lang="en">c.lloyd@auckland.ac.nz</rdf:value><rdf:type><rdf:Description rdf:about="http://imc.org/vCard/3.0#internet"/></rdf:type></rdf:Description><rdf:Description rdf:about="rdf:#8c73d2c9-42f5-4bdc-af90-748f573ae418"><modified xmlns="http://purl.org/dc/terms/"><rdf:Description rdf:about="rdf:#e76d4e28-fe06-4e5c-8ab5-eed6f0940699"/></modified><cmeta:modifier><rdf:Description rdf:about="rdf:#8e025f2d-dfe3-4690-9747-764897912e28"/></cmeta:modifier><rdf:value xml:lang="en">added units</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#4b7658cc-4144-479a-aaf7-cf86bdb397a2"><FN xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine Lloyd</FN></rdf:Description><rdf:Description rdf:about="rdf:#f9d7d9cb-3df8-452c-bb87-759019c5fa20"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">May</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Lloyd</Family></rdf:Description><rdf:Description rdf:about="rdf:#880edbc7-d252-4c09-a3a8-c1512690adf9"><FN xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine Lloyd</FN></rdf:Description><rdf:Description rdf:about="rdf:#21c41487-8a28-4beb-b96d-729d974a2d0e"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2007-07-16T00:00:00+00:00</W3CDTF></rdf:Description><rdf:Description rdf:about=""><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Infection dynamics in HIV-specific CD4 T cells: Does a CD4 T cell boost benefit the host or the virus (Model 2)</title><cmeta:comment><rdf:Description rdf:about="rdf:#796d810e-2fcc-42ca-a4c3-f175f07fca75"/></cmeta:comment><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:#21c41487-8a28-4beb-b96d-729d974a2d0e"/></created><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#2f0302e6-a1ba-4289-ae0e-3e683702cd00"/></creator><cmeta:modification><rdf:Description rdf:about="rdf:#8c73d2c9-42f5-4bdc-af90-748f573ae418"/></cmeta:modification></rdf:Description><rdf:Description rdf:about="rdf:#2be71aa3-67df-4bf5-ba2a-edaae86a999a"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">H</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Dean</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Hamer</Family></rdf:Description><rdf:Description rdf:about="rdf:#633015ce-17da-408e-9d22-4040b92dc853"><rdf:_1><rdf:Description rdf:about="rdf:#160a60fc-7260-4c13-a11c-7f055d412a6e"/></rdf:_1><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:#b119fd3e-05bf-4a7f-9655-cb6731fa5953"/></rdf:_2></rdf:Description><rdf:Description rdf:about="rdf:#ccd516c1-6db0-4187-91f8-84a358b4f7d5"><Other xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">May</Other><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Catherine</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Lloyd</Family></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 HIV-specific CD4+ T cells</alternative></rdf:Description><rdf:Description rdf:about="rdf:#8e025f2d-dfe3-4690-9747-764897912e28"><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#ccd516c1-6db0-4187-91f8-84a358b4f7d5"/></N></rdf:Description><rdf:Description rdf:about="#v"><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">v</title><alternative xmlns="http://purl.org/dc/terms/" xml:lang="en">free virus particles</alternative></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 HIV-specific CD4+ T cells</alternative></rdf:Description><rdf:Description rdf:about="rdf:#4b4520ce-8e7d-4729-83ab-fbc1da78dcdc"><Given xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Dominik</Given><Family xmlns="http://www.w3.org/2001/vcard-rdf/3.0#" xml:lang="en">Wodarz</Family></rdf:Description><rdf:Description rdf:about="rdf:#dede96b7-e6bf-4054-a3bb-bf911b231eab"><subject xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#2ccba2c3-dc0f-4c94-b10d-fee8c2157e89"/></subject></rdf:Description><rdf:Description rdf:about="rdf:#b119fd3e-05bf-4a7f-9655-cb6731fa5953"><rdf:type><rdf:Description rdf:about="http://www.cellml.org/bqs/1.0#Person"/></rdf:type><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#2be71aa3-67df-4bf5-ba2a-edaae86a999a"/></N></rdf:Description><rdf:Description rdf:about="rdf:#e76d4e28-fe06-4e5c-8ab5-eed6f0940699"><W3CDTF xmlns="http://purl.org/dc/terms/" xml:lang="en">2007-09-06T13:39:32+12:00</W3CDTF></rdf:Description><rdf:Description rdf:about="rdf:#4cce23c8-f8dc-4586-acfb-aed50d513e53"><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">The Bioengineering Institute</Orgunit></rdf:Description><rdf:Description rdf:about="#wodarz_2007"><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#dede96b7-e6bf-4054-a3bb-bf911b231eab"/></reference><reference xmlns="http://www.cellml.org/bqs/1.0#"><rdf:Description rdf:about="rdf:#26118a9d-6018-4598-855d-10953ac95edd"/></reference><cmeta:comment><rdf:Description rdf:about="rdf:#ddf33ce8-3208-4551-be81-406b9fe2fe76"/></cmeta:comment><title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">
        Wodarz and Hamer's 2007 mathematical model of infection dynamics in HIV-specific CD4+ T cells.
      </title></rdf:Description><rdf:Description rdf:about="rdf:#2f0302e6-a1ba-4289-ae0e-3e683702cd00"><EMAIL xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#665b4094-dc8e-4545-babd-39d7d81cf26b"/></EMAIL><ORG xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#4cce23c8-f8dc-4586-acfb-aed50d513e53"/></ORG><N xmlns="http://www.w3.org/2001/vcard-rdf/3.0#"><rdf:Description rdf:about="rdf:#f9d7d9cb-3df8-452c-bb87-759019c5fa20"/></N></rdf:Description><rdf:Description rdf:about="rdf:#796d810e-2fcc-42ca-a4c3-f175f07fca75"><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#880edbc7-d252-4c09-a3a8-c1512690adf9"/></creator><rdf:value xml:lang="en">The model runs in PCEnv to replicate the published results.</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#2ccba2c3-dc0f-4c94-b10d-fee8c2157e89"><subject_type xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">keyword</subject_type><rdf:value><rdf:Description rdf:about="rdf:#983a601a-7eb7-40cc-9d48-b5b90f165a94"/></rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#ddf33ce8-3208-4551-be81-406b9fe2fe76"><creator xmlns="http://purl.org/dc/elements/1.1/"><rdf:Description rdf:about="rdf:#4b7658cc-4144-479a-aaf7-cf86bdb397a2"/></creator><rdf:value xml:lang="en">This is a CellML description of Wodarz and Hamer's 2007 mathematical model of infection dynamics in HIV-specific CD4+ T cells.</rdf:value></rdf:Description><rdf:Description rdf:about="rdf:#983a601a-7eb7-40cc-9d48-b5b90f165a94"><rdf:_1 xml:lang="en">immunology</rdf:_1><rdf:type><rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#Bag"/></rdf:type><rdf:_3 xml:lang="en">HIV</rdf:_3><rdf:_2 xml:lang="en">viral dynamics</rdf:_2><rdf:_4 xml:lang="en">CD4+ T cell</rdf:_4></rdf:Description></rdf:RDF></model>