Rendering of the source text

<?xml version='1.0' encoding='utf-8'?>
<!--  FILE :  grossman_model_1998.xml

CREATED :  4th December 2003

LAST MODIFIED : 4th December 2003

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 16/1/02 CellML Metadata 1.0 Specification.

DESCRIPTION :  This file contains a CellML description of Grossman et al.'s 1998 mathematical model of plasma virus kinetics following therapy.
CHANGES:  
  
--><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="grossman_feinberg_kuznetsov_dimitrov_paul_1998_version01" name="grossman_feinberg_kuznetsov_dimitrov_paul_1998_version01">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
  <articleinfo>
  <title>Modelling the Kinetics of Plasma Virus Following the Initiation of Therapy</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>
Highly active anti-retroviral therapy (HAART) significantly reduces the viral load in most HIV infected patients.  Most believe that this is due to the drug's ability to act as an efficient blockade of the <emphasis>de novo</emphasis> infection of target cells.  However, HAART is not 100 percent effective, usually because some long-lived infected cells persist, which then convert to short-lived HIV producers when activated.  The extent to which virus production from infected to uninfected cells is blocked is of great importance.  The answer will help to determine whether or not HAART is capable of eradicating HIV infection.
</para>

<para>
The concept that drug treatment is an efficient blockade of viral replication has derived much of its credibility from being incorporated into a model that successfully fits the kinetic data.  This model of HIV dynamics was published by <ulink url="${HTML_EXMPL_PERELSON_MODEL}">Perelson <emphasis>et al.</emphasis> in 1996</ulink>.  Their main observation was that viral load decline following drug application occurred in two discrete phases: an initial rapid decline (phase I) followed by a more gradual decline (phase II).  They explained this observation by the fact that the drugs decreased viral load by inhibiting the <emphasis>de novo</emphasis> infection of susceptible cells.  Phase I reflected the decline of the originally infected cells, and phase II reflected the decline of those infected cells which had a slightly longer half-life.
</para>

<para>
However, the authors of the current model, Grossman <emphasis>et al.</emphasis> argue that the idea of a cell having a half-life is biologically implausible.  They suggest instead that it is more plausible to think of the infected lymphocytes undergoing an aging-like process.  That is, the death of an infected, HIV-producing cell follows productive infection after a time delay (see <xref linkend="fig_cell_diagram"/> below).  The observed exponential decline in viral load then requires an alternative explanation.  This is provided by assuming that <emphasis>de novo</emphasis> infection is not blocked completely by HAART, but only reduced.   
</para> 

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

<para>
<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6VHW-3V5VD9Y-C&amp;_user=140507&amp;_coverDate=11%2F01%2F1998&amp;_alid=132243356&amp;_rdoc=1&amp;_fmt=summary&amp;_orig=search&amp;_qd=1&amp;_cdi=6077&amp;_sort=d&amp;_docanchor=&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=bd6c63528fd70efcdefe0d2be162ea9f">HIV infection: how effective is drug combination treatment?</ulink>, Zvi Grossman, Mark Feinberg, Vladimir Kuznetsov, Dimiter Dimitrov, and William Paul, 1998, <ulink url="http://www.sciencedirect.com/science?_ob=JournalURL&amp;_cdi=6077&amp;_auth=y&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=97e17db3f48862ce8ba63183f14ecd55">
            <emphasis>Immunology Today</emphasis>
          </ulink>, 19, 528-532.  (<ulink url="http://www.sciencedirect.com/science?_ob=ArticleURL&amp;_udi=B6VHW-3V5VD9Y-C&amp;_user=140507&amp;_coverDate=11%2F01%2F1998&amp;_alid=132243356&amp;_rdoc=1&amp;_fmt=full&amp;_orig=search&amp;_qd=1&amp;_cdi=6077&amp;_sort=d&amp;_docanchor=&amp;view=c&amp;_acct=C000011498&amp;_version=1&amp;_urlVersion=0&amp;_userid=140507&amp;md5=73cecab5084cdcdc9ae558e99e9a43b6">Full text (HTML)</ulink> and PDF versions of the article are available on the <emphasis>Immunology Today</emphasis> website.)  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=9818549&amp;dopt=Abstract">PubMed ID: 9818549</ulink>
</para>

<informalfigure float="0" id="fig_cell_diagram">
<mediaobject>
  <imageobject>
    <objectinfo>
      <title>cell diagram</title>
    </objectinfo>
    <imagedata fileref="grossman_1998.png"/>
  </imageobject>
</mediaobject>
<caption>Schematic diagram of the conceptual model representing the cycles of infection of activated, susceptible cells (S), with delay-type kinetics of infected cell death.  V represents the ambient virus, and I<subscript>j</subscript> represents the infected cells in the various different stages of infection.</caption>
</informalfigure>

<para>
Model simulations revealed that the half-life of the infected cells can be calculated with reasonable accuracy from clinical data.  However, the remaining parameters can not be accurately predicted from the current model, more data is needed.     
</para>

<para>
A variable delay from productive cell infection to cell death can be modelled by dividing the process into several sequential stages.  These stages may represent real stages in the infection process, or they may be regarded as a modelling convenience.  Another method of modelling a variable delay is to introduce a distribution of delay times around a fixed average.  This is the approach chosen by the authors of the current model.
</para>

</sect1>
</article>
</documentation>
  
  
  <units name="per_ml">
    <unit units="litre" prefix="milli" exponent="-1"/>
  </units>
  
  <units name="day">
    <unit units="second" exponent="-1" multiplier="86400.0"/>
  </units>
  
  <units name="first_order_rate_constant">
    <unit units="day" exponent="-1"/>
  </units>
  
  
  <component name="environment">
    <variable units="day" public_interface="out" name="time"/>
  </component>
  
  <component name="kinetic_parameters">
    <variable units="first_order_rate_constant" public_interface="out" name="k" initial_value="2.76"/>
    <variable units="first_order_rate_constant" public_interface="out" name="c"/>
    <variable units="first_order_rate_constant" public_interface="out" name="p"/>
    <variable units="first_order_rate_constant" public_interface="out" name="q" initial_value="3.0"/>
    <variable units="first_order_rate_constant" public_interface="out" name="b" initial_value="1.0"/>
    <variable units="first_order_rate_constant" public_interface="out" name="a"/>
  </component>
  
  <component cmeta:id="S" name="S">
    <rdf:RDF>
      <rdf:Description rdf:about="S">
        <dc:title>S</dc:title>
        <dcterms:alternative>susceptible cells</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="S"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="a"/>
    <variable units="first_order_rate_constant" public_interface="in" name="b"/>
    <variable units="first_order_rate_constant" public_interface="in" name="c"/>
    <variable units="per_ml" public_interface="in" name="V"/>
    <variable units="day" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>S</ci> 
        </apply>
        <apply>
          <minus/>
          <ci> a </ci>
          <apply>
            <plus/>
            <apply>
              <times/>
              <ci> b </ci>
              <ci> S </ci>
            </apply> 
            <apply>
              <times/>
              <ci> c </ci>
              <ci> S </ci>
              <ci> V </ci>
            </apply>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="I1" name="I1">
    <rdf:RDF>
      <rdf:Description rdf:about="I1">
        <dc:title>I1</dc:title>
        <dcterms:alternative>infected cell stage 1</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="I1"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="c"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k"/>
    <variable units="per_ml" public_interface="in" name="V"/>
    <variable units="per_ml" public_interface="in" name="S"/>
    <variable units="day" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>I1</ci> 
        </apply>
        <apply>
          <minus/>
          <apply>
            <times/>
            <ci> c </ci>
            <ci> S </ci>
            <ci> V </ci>
          </apply> 
          <apply>
            <times/>
            <ci> k </ci>
            <ci> I1 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="I2" name="I2">
    <rdf:RDF>
      <rdf:Description rdf:about="I2">
        <dc:title>I2</dc:title>
        <dcterms:alternative>infected cell stage 2</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="I2"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="k"/>
    <variable units="per_ml" public_interface="in" name="I1"/>
    <variable units="day" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>I2</ci> 
        </apply>
        <apply>
          <times/>
          <ci> k </ci>
          <apply>
            <minus/>
            <ci> I1 </ci>
            <ci> I2 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component> 
  
  <component cmeta:id="I3" name="I3">
    <rdf:RDF>
      <rdf:Description rdf:about="I3">
        <dc:title>I3</dc:title>
        <dcterms:alternative>infected cell stage 3</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="I3"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="k"/>
    <variable units="per_ml" public_interface="in" name="I2"/>
    <variable units="day" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>I3</ci> 
        </apply>
        <apply>
          <times/>
          <ci> k </ci>
          <apply>
            <minus/>
            <ci> I2 </ci>
            <ci> I3 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="I4" name="I4">
    <rdf:RDF>
      <rdf:Description rdf:about="I4">
        <dc:title>I4</dc:title>
        <dcterms:alternative>infected cell stage 4</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="I4"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="k"/>
    <variable units="per_ml" public_interface="in" name="I3"/>
    <variable units="day" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>I4</ci> 
        </apply>
        <apply>
          <times/>
          <ci> k </ci>
          <apply>
            <minus/>
            <ci> I3 </ci>
            <ci> I4 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="I5" name="I5">
    <rdf:RDF>
      <rdf:Description rdf:about="I5">
        <dc:title>I5</dc:title>
        <dcterms:alternative>infected cell stage 5</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="I5"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="k"/>
    <variable units="per_ml" public_interface="in" name="I4"/>
    <variable units="day" public_interface="in" name="time"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <apply>
          <diff/> 
          <bvar>
            <ci>time</ci>
          </bvar> 
          <ci>I5</ci> 
        </apply>
        <apply>
          <times/>
          <ci> k </ci>
          <apply>
            <minus/>
            <ci> I4 </ci>
            <ci> I5 </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="V" name="V">
    <rdf:RDF>
      <rdf:Description rdf:about="V">
        <dc:title>V</dc:title>
        <dcterms:alternative>ambient virus</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="V"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="p"/>
    <variable units="first_order_rate_constant" public_interface="in" name="q"/>
    <variable units="per_ml" public_interface="in" name="I5"/>
    <variable units="day" public_interface="in" name="time"/>
    
    <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> p </ci>
            <ci> I5 </ci>
          </apply> 
          <apply>
            <times/>
            <ci> q </ci>
            <ci> V </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
    
  <component cmeta:id="Se" name="Se">
    <rdf:RDF>
      <rdf:Description rdf:about="Se">
        <dc:title>Se</dc:title>
        <dcterms:alternative>steady-state susceptible cells</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="Se"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="q"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k"/>
    <variable units="first_order_rate_constant" public_interface="in" name="p"/>
    <variable units="first_order_rate_constant" public_interface="in" name="c"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>Se</ci> 
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> q </ci>
            <ci> k </ci>
          </apply> 
          <apply>
            <times/>
            <ci> p </ci>
            <ci> c </ci>
          </apply>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="Ve" name="Ve">
    <rdf:RDF>
      <rdf:Description rdf:about="Ve">
        <dc:title>Ve</dc:title>
        <dcterms:alternative>steady-state viral load</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="Ve"/>
    
    <variable units="dimensionless" name="R0"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="a"/>
    <variable units="first_order_rate_constant" public_interface="in" name="b"/>
    <variable units="first_order_rate_constant" public_interface="in" name="p"/>
    <variable units="first_order_rate_constant" public_interface="in" name="c"/>
    <variable units="first_order_rate_constant" public_interface="in" name="q"/>
    <variable units="first_order_rate_constant" public_interface="in" name="k"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>Ve</ci>
        <apply>
          <times/> 
          <apply>
            <divide/>
            <ci> b </ci>
            <ci> c </ci>
          </apply> 
          <apply>
            <minus/>
            <ci> R0 </ci>
            <cn cellml:units="dimensionless"> 1.0 </cn>
          </apply>
        </apply>
      </apply>
      
      <apply>
        <eq/> 
        <ci>R0</ci> 
        <apply>
          <divide/>
          <apply>
            <times/>
            <ci> a </ci>
            <ci> p </ci>
            <ci> c </ci>
          </apply> 
          <apply>
            <times/>
            <ci> b </ci>
            <ci> q </ci>
            <ci> k </ci>
          </apply>
        </apply>
      </apply>     
    </math>
  </component>
  
  <component cmeta:id="I1e" name="I1e">
    <rdf:RDF>
      <rdf:Description rdf:about="I1e">
        <dc:title>I1e</dc:title>
        <dcterms:alternative>steady-state infected cell stage 1</dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="I1e"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="q"/>
    <variable units="first_order_rate_constant" public_interface="in" name="p"/>
    <variable units="per_ml" public_interface="in" name="Ve"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>I1e</ci>
        <apply>
          <times/> 
          <apply>
            <divide/>
            <ci> q </ci>
            <ci> p </ci>
          </apply> 
          <ci> Ve </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="I2e" name="I2e">
    <rdf:RDF>
      <rdf:Description rdf:about="I2e">
        <dc:title>I2e</dc:title>
        <dcterms:alternative>
          steady-state infected cell stage 2
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="I2e"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="q"/>
    <variable units="first_order_rate_constant" public_interface="in" name="p"/>
    <variable units="per_ml" public_interface="in" name="Ve"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>I2e</ci>
        <apply>
          <times/> 
          <apply>
            <divide/>
            <ci> q </ci>
            <ci> p </ci>
          </apply> 
          <ci> Ve </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="I3e" name="I3e">
    <rdf:RDF>
      <rdf:Description rdf:about="I3e">
        <dc:title>I3e</dc:title>
        <dcterms:alternative>
          steady-state infected cell stage 1
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="I3e"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="q"/>
    <variable units="first_order_rate_constant" public_interface="in" name="p"/>
    <variable units="per_ml" public_interface="in" name="Ve"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>I3e</ci>
        <apply>
          <times/> 
          <apply>
            <divide/>
            <ci> q </ci>
            <ci> p </ci>
          </apply> 
          <ci> Ve </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="I4e" name="I4e">
    <rdf:RDF>
      <rdf:Description rdf:about="I4e">
        <dc:title>I4e</dc:title>
        <dcterms:alternative>
          steady-state infected cell stage 1
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="I4e"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="q"/>
    <variable units="first_order_rate_constant" public_interface="in" name="p"/>
    <variable units="per_ml" public_interface="in" name="Ve"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>I4e</ci>
        <apply>
          <times/> 
          <apply>
            <divide/>
            <ci> q </ci>
            <ci> p </ci>
          </apply> 
          <ci> Ve </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  <component cmeta:id="I5e" name="I5e">
    <rdf:RDF>
      <rdf:Description rdf:about="I5e">
        <dc:title>I5e</dc:title>
        <dcterms:alternative>
          steady-state infected cell stage 1
        </dcterms:alternative>  
      </rdf:Description>
    </rdf:RDF>  
    <variable units="per_ml" public_interface="out" name="I5e"/>
    
    <variable units="first_order_rate_constant" public_interface="in" name="q"/>
    <variable units="first_order_rate_constant" public_interface="in" name="p"/>
    <variable units="per_ml" public_interface="in" name="Ve"/>
    
    <math xmlns="http://www.w3.org/1998/Math/MathML"> 
      <apply>
        <eq/> 
        <ci>I5e</ci>
        <apply>
          <times/> 
          <apply>
            <divide/>
            <ci> q </ci>
            <ci> p </ci>
          </apply> 
          <ci> Ve </ci>
        </apply>
      </apply>    
    </math>
  </component>
  
  
  <connection>
    <map_components component_2="environment" component_1="S"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="I1"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="I2"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="I3"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="I4"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="I5"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="environment" component_1="V"/>
    <map_variables variable_2="time" variable_1="time"/>
  </connection>
  
  <connection>
    <map_components component_2="V" component_1="S"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="S" component_1="I1"/>
    <map_variables variable_2="S" variable_1="S"/>
  </connection>
  
  <connection>
    <map_components component_2="V" component_1="I1"/>
    <map_variables variable_2="V" variable_1="V"/>
  </connection>
  
  <connection>
    <map_components component_2="I1" component_1="I2"/>
    <map_variables variable_2="I1" variable_1="I1"/>
  </connection>
  
  <connection>
    <map_components component_2="I2" component_1="I3"/>
    <map_variables variable_2="I2" variable_1="I2"/>
  </connection>
  
  <connection>
    <map_components component_2="I3" component_1="I4"/>
    <map_variables variable_2="I3" variable_1="I3"/>
  </connection>
  
  <connection>
    <map_components component_2="I4" component_1="I5"/>
    <map_variables variable_2="I4" variable_1="I4"/>
  </connection>
  
  <connection>
    <map_components component_2="I5" component_1="V"/>
    <map_variables variable_2="I5" variable_1="I5"/>
  </connection>
  
  <connection>
    <map_components component_2="Ve" component_1="I1e"/>
    <map_variables variable_2="Ve" variable_1="Ve"/>
  </connection>
  
  <connection>
    <map_components component_2="Ve" component_1="I2e"/>
    <map_variables variable_2="Ve" variable_1="Ve"/>
  </connection>
  
  <connection>
    <map_components component_2="Ve" component_1="I3e"/>
    <map_variables variable_2="Ve" variable_1="Ve"/>
  </connection>
  
  <connection>
    <map_components component_2="Ve" component_1="I4e"/>
    <map_variables variable_2="Ve" variable_1="Ve"/>
  </connection>
  
  <connection>
    <map_components component_2="Ve" component_1="I5e"/>
    <map_variables variable_2="Ve" variable_1="Ve"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="S"/>
    <map_variables variable_2="a" variable_1="a"/>
    <map_variables variable_2="b" variable_1="b"/>
    <map_variables variable_2="c" variable_1="c"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="I1"/>
    <map_variables variable_2="c" variable_1="c"/>
    <map_variables variable_2="k" variable_1="k"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="I2"/>
    <map_variables variable_2="k" variable_1="k"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="I3"/>
    <map_variables variable_2="k" variable_1="k"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="I4"/>
    <map_variables variable_2="k" variable_1="k"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="I5"/>
    <map_variables variable_2="k" variable_1="k"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="V"/>
    <map_variables variable_2="p" variable_1="p"/>
    <map_variables variable_2="q" variable_1="q"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="Se"/>
    <map_variables variable_2="p" variable_1="p"/>
    <map_variables variable_2="q" variable_1="q"/>
    <map_variables variable_2="k" variable_1="k"/>
    <map_variables variable_2="c" variable_1="c"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="Ve"/>
    <map_variables variable_2="a" variable_1="a"/>
    <map_variables variable_2="b" variable_1="b"/>
    <map_variables variable_2="c" variable_1="c"/>
    <map_variables variable_2="p" variable_1="p"/>
    <map_variables variable_2="q" variable_1="q"/>
    <map_variables variable_2="k" variable_1="k"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="I1e"/>
    <map_variables variable_2="p" variable_1="p"/>
    <map_variables variable_2="q" variable_1="q"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="I2e"/>
    <map_variables variable_2="p" variable_1="p"/>
    <map_variables variable_2="q" variable_1="q"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="I3e"/>
    <map_variables variable_2="p" variable_1="p"/>
    <map_variables variable_2="q" variable_1="q"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="I4e"/>
    <map_variables variable_2="p" variable_1="p"/>
    <map_variables variable_2="q" variable_1="q"/>
  </connection>
  
  <connection>
    <map_components component_2="kinetic_parameters" component_1="I5e"/>
    <map_variables variable_2="p" variable_1="p"/>
    <map_variables variable_2="q" variable_1="q"/>
  </connection>
  

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
  <rdf:Bag rdf:about="rdf:#436edefe-acab-4b08-b7cf-61b92d8e79c5">
    <rdf:li>immunology</rdf:li>
    <rdf:li>virus dynamics</rdf:li>
    <rdf:li>viral dynamics</rdf:li>
    <rdf:li>hiv-1</rdf:li>
    <rdf:li>therapy</rdf:li>
    <rdf:li>drug combination therapy</rdf:li>
    <rdf:li>pathology</rdf:li>
  </rdf:Bag>
  <rdf:Seq rdf:about="rdf:#0e0b20fa-26e7-4e88-b55f-cea066f8159d">
    <rdf:li rdf:resource="rdf:#4f28cac8-d7e2-4004-8cf1-fe5799e94a57"/>
    <rdf:li rdf:resource="rdf:#ce5c4d5c-42bd-4818-b8bc-1e8c754759eb"/>
    <rdf:li rdf:resource="rdf:#fc4a5a14-5e51-407a-ad0a-080d0a710ee1"/>
    <rdf:li rdf:resource="rdf:#01b83260-21b4-4b83-af15-8bc90ceaea43"/>
    <rdf:li rdf:resource="rdf:#29ce500d-3d5e-41be-afdd-6948f6bf40b3"/>
  </rdf:Seq>
  <rdf:Description rdf:about="rdf:#9e4f5a07-d5bc-4679-a16d-e65dd56c94cb">
    <vCard:FN>Catherine Lloyd</vCard:FN>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#8d571dbd-87f6-4d7d-8823-9db2479397be">
    <vCard:Given>Dimiter</vCard:Given>
    <vCard:Family>Dimitrov</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#29ce500d-3d5e-41be-afdd-6948f6bf40b3">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#b59b2e63-a3df-4613-81b4-5dc6c08e6f0e"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#744d5c25-61ad-4940-95d3-093569764878">
    <bqs:Pubmed_id>9818549</bqs:Pubmed_id>
    <bqs:JournalArticle rdf:resource="rdf:#16188414-2fbe-45ca-bd83-a84da9ee9330"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#cbad3d1e-a50a-4552-889e-2bf873937675">
    <vCard:Given>Zvi</vCard:Given>
    <vCard:Family>Grossman</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5a95ab2a-3715-4534-be13-0834f103fba1">
    <vCard:Given>Vladimir</vCard:Given>
    <vCard:Family>Kuznetsov</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#fc4a5a14-5e51-407a-ad0a-080d0a710ee1">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#5a95ab2a-3715-4534-be13-0834f103fba1"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4d982326-2542-4687-8480-4b660a8a22e5">
    <dc:subject rdf:resource="rdf:#0e4ceee9-e52f-4257-a05d-203cc59ff61c"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#b59b2e63-a3df-4613-81b4-5dc6c08e6f0e">
    <vCard:Given>William</vCard:Given>
    <vCard:Family>Paul</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#cf557a80-6fa9-421b-a38a-22ce1edf0073">
    <dcterms:W3CDTF>2003-12-04</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#01b83260-21b4-4b83-af15-8bc90ceaea43">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#8d571dbd-87f6-4d7d-8823-9db2479397be"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#5ba63572-dadf-4968-a3ba-0f04696ca614">
    <dc:title>Immunology Today</dc:title>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#2807ba9a-de24-44c9-930b-ec24a795c868">
    <vCard:ORG rdf:resource="rdf:#a8541ab9-6da1-45e0-ace0-b9de9f05204d"/>
    <vCard:EMAIL rdf:resource="rdf:#e5308165-389d-4670-b63f-89f35369207e"/>
    <vCard:N rdf:resource="rdf:#441f1a8b-3b65-4fb0-99ef-4cf7081a4d6b"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#4f28cac8-d7e2-4004-8cf1-fe5799e94a57">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#cbad3d1e-a50a-4552-889e-2bf873937675"/>
  </rdf:Description>
  <rdf:Description rdf:about="#grossman_feinberg_kuznetsov_dimitrov_paul_1998_version01">
    <dc:title>
        Grossman et al.'s 1998 mathematical model of plasma virus kinetics 
        following therapy.
      </dc:title>
    <cmeta:comment rdf:resource="rdf:#f1046e28-b8ec-45a3-abc7-60065ebcad87"/>
    <bqs:reference rdf:resource="rdf:#4d982326-2542-4687-8480-4b660a8a22e5"/>
    <bqs:reference rdf:resource="rdf:#744d5c25-61ad-4940-95d3-093569764878"/>
  </rdf:Description>
  <rdf:Description rdf:about="">
    <dc:publisher>
        The University of Auckland, Bioengineering Institute
      </dc:publisher>
    <dcterms:created rdf:resource="rdf:#cf557a80-6fa9-421b-a38a-22ce1edf0073"/>
    <dc:creator rdf:resource="rdf:#2807ba9a-de24-44c9-930b-ec24a795c868"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#0e4ceee9-e52f-4257-a05d-203cc59ff61c">
    <bqs:subject_type>keyword</bqs:subject_type>
    <rdf:value rdf:resource="rdf:#436edefe-acab-4b08-b7cf-61b92d8e79c5"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#9454d2f2-e68a-4b5c-a645-24ee9f91ef90">
    <vCard:Given>Mark</vCard:Given>
    <vCard:Family>Feinberg</vCard:Family>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#441f1a8b-3b65-4fb0-99ef-4cf7081a4d6b">
    <vCard:Given>Catherine</vCard:Given>
    <vCard:Family>Lloyd</vCard:Family>
    <vCard:Other>May</vCard:Other>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#f1046e28-b8ec-45a3-abc7-60065ebcad87">
    <dc:creator rdf:resource="rdf:#9e4f5a07-d5bc-4679-a16d-e65dd56c94cb"/>
    <rdf:value>
          This is the CellML description of Grossman et al.'s 1998 mathematical 
          model of plasma virus kinetics following therapy.
        </rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#e5308165-389d-4670-b63f-89f35369207e">
    <rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
    <rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#2c48f902-cc13-4d33-9056-63661d40ba40">
    <dcterms:W3CDTF>1998-11-01</dcterms:W3CDTF>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#16188414-2fbe-45ca-bd83-a84da9ee9330">
    <dc:creator rdf:resource="rdf:#0e0b20fa-26e7-4e88-b55f-cea066f8159d"/>
    <dc:title>
            HIV infection: how effective is drug combination treatment?
          </dc:title>
    <bqs:volume>19</bqs:volume>
    <bqs:first_page>528</bqs:first_page>
    <bqs:Journal rdf:resource="rdf:#5ba63572-dadf-4968-a3ba-0f04696ca614"/>
    <dcterms:issued rdf:resource="rdf:#2c48f902-cc13-4d33-9056-63661d40ba40"/>
    <bqs:last_page>532</bqs:last_page>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#ce5c4d5c-42bd-4818-b8bc-1e8c754759eb">
    <rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
    <vCard:N rdf:resource="rdf:#9454d2f2-e68a-4b5c-a645-24ee9f91ef90"/>
  </rdf:Description>
  <rdf:Description rdf:about="rdf:#a8541ab9-6da1-45e0-ace0-b9de9f05204d">
    <vCard:Orgname>The University of Auckland</vCard:Orgname>
    <vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
  </rdf:Description>
</rdf:RDF>
</model>