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<!-- documentation -->
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Population dynamics of immune responses to persistent viruses</title>
<author>
<firstname>Ethan</firstname>
<surname>Choi</surname>
<affiliation>
<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>This model has been built with the differential expressions in Nowak's 1996 paper for population dynamics of immune responses to persistent viruses and is known to run in PCEnv and COR. The units have been checked and they are consistent. This particular CellML model is the 1st model out of the 3 outlined in the paper. Note that the figures in the paper display the logged varibale values, and also certain parameters are unspecified and are left for the modeller to decide. Current parameterization portrays the interaction of uninfected cells x, infected cells y, and free virus particles v (model 1).</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>Abstract: Mathematical models, which are based on a firm understanding of biological interactions, can provide nonintuitive insights into the dynamics of host responses to infectious agents and can suggest new avenues for experimentation. Here, a simple mathematical approach is developed to explore the relation between antiviral immune responses, virus load, and virus diversity. The model results are compared to data on cytotoxic T cell responses and viral diversity in infections with the human T cell leukemia virus (HTLV-1) and the human immunodeficiency virus (HIV-1).</para>
<para>
Population dynamics of immune responses to persistent viruses, Nowak, MA and Bangham, CR, 1996, <emphasis>Science</emphasis>
, 272, 74-79 <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/8600540">PubMed ID: 8600540</ulink>
</para>
<informalfigure float="0" id="______">
<mediaobject>
<imageobject>
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<title>Model Diagram</title>
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<caption>Schematic diagram of a model for virus-CTL interaction.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<!-- units -->
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<unit multiplier="86400" units="second"/>
</units>
<units name="first_order_rate_constant">
<unit exponent="-1" units="day"/>
</units>
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<variable cmeta:id="environment_time" name="time" public_interface="out" units="day"/>
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<rdf:Description rdf:about="#uninfected">This component stores information related to the uninfected cell population</rdf:Description>
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<times/>
<ci>beta</ci>
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<component cmeta:id="infected" name="infected">
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#infected">This component stores information related to the infected cell population</rdf:Description>
<rdf:Description rdf:about="#y">infected cells</rdf:Description>
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<variable name="time" public_interface="in" units="day"/>
<variable initial_value="0.05" name="beta" public_interface="out" units="first_order_rate_constant"/>
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<ci>a</ci>
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</component>
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<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#virus">This component stores information related to the population of free virus particles</rdf:Description>
<rdf:Description rdf:about="#v">free virus particles</rdf:Description>
</rdf:RDF>
<variable name="time" public_interface="in" units="day"/>
<variable initial_value="1" name="k" units="first_order_rate_constant"/>
<variable initial_value="1" name="u" units="first_order_rate_constant"/>
<variable name="y" public_interface="in" units="dimensionless"/>
<variable cmeta:id="v" initial_value="5" name="v" public_interface="out" units="dimensionless"/>
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<ci>k</ci>
<ci>y</ci>
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<apply>
<times/>
<ci>u</ci>
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<!-- connections -->
<connection>
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<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="infected"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="virus"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="uninfected" component_2="virus"/>
<map_variables variable_1="v" variable_2="v"/>
</connection>
<connection>
<map_components component_1="infected" component_2="uninfected"/>
<map_variables variable_1="x" variable_2="x"/>
<map_variables variable_1="beta" variable_2="beta"/>
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<connection>
<map_components component_1="infected" component_2="virus"/>
<map_variables variable_1="v" variable_2="v"/>
<map_variables variable_1="y" variable_2="y"/>
</connection>
<!-- metadata -->
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<rdf:_3 xml:lang="en">virus load</rdf:_3>
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</rdf:type>
<rdf:_7 xml:lang="en">HTLV-1</rdf:_7>
<rdf:_8 xml:lang="en">HIV-1</rdf:_8>
<rdf:_6 xml:lang="en">CTL</rdf:_6>
<rdf:_5 xml:lang="en">mutation</rdf:_5>
<rdf:_2 xml:lang="en">antiviral immune response</rdf:_2>
<rdf:_1 xml:lang="en">immunology </rdf:_1>
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<title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en">Population dynamics of immune responses to persistent viruses (Model 1)</title>
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<last_page xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">79</last_page>
<title xmlns="http://purl.org/dc/elements/1.1/" xml:lang="en"> Population dynamics of immune responses to persistent viruses </title>
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<volume xmlns="http://www.cellml.org/bqs/1.0#" xml:lang="en">272</volume>
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