<?xml version="1.0"?>

<!--  FILE :  wodarz_model_II_03.xml

CREATED :  17th December 2003

LAST MODIFIED : 17th 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 Wodarz's 2nd 2003 mathematical model of the evolution of immunological memory and the regulation of competition between pathogens.

CHANGES:  
  
-->


<model name="wodarz_model_II_03" cmeta:id="wodarz_model_II_03" xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" xmlns:cmeta="http://www.cellml.org/metadata/1.0#">
  
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bqs="http://www.cellml.org/bqs/1.0#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">
    
<!--
      The following RDF block contains metadata that applies to this document
      as a whole, as indicated by the empty about attribute on the 
      <rdf:Description> element.
    -->

    
<rdf:Description rdf:about="">
      
<!--
        The Model Builder Metadata.  The Dublin Core "creator" element is used  
        to indicate the person who translated the model into CellML.
      -->

      
<dc:creator rdf:parseType="Resource">
        
<vCard:N rdf:parseType="Resource">
          
<vCard:Family>Lloyd</vCard:Family>
          
<vCard:Given>Catherine</vCard:Given>
          
<vCard:Other>May</vCard:Other>
        
</vCard:N>
        
<vCard:EMAIL rdf:parseType="Resource">
          
<rdf:value>c.lloyd@auckland.ac.nz</rdf:value>
          
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet" />
        
</vCard:EMAIL>
        
<vCard:ORG rdf:parseType="Resource">
          
<vCard:Orgname>The University of Auckland</vCard:Orgname>
          
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
        
</vCard:ORG>
      
</dc:creator>
      
      
<!--
        The Creation Date metadata. This is the date on which the model
        was translated into CellML.
      -->

      
<dcterms:created rdf:parseType="Resource">
        
<dcterms:W3CDTF>2003-12-17</dcterms:W3CDTF>
      
</dcterms:created>
      
      
<!--
        The Modification History metadata. This lists the changes that have been
        made to the document, who made the changes, and when they were made.
      -->

      
      
<!-- The Publisher metadata. -->
      
<dc:publisher>
        The University of Auckland, Bioengineering Institute
      
</dc:publisher>
    
</rdf:Description>
    
    
<!--
      The following metadata refers to the model itself, as indicated by the
      reference to the ID "wodarz_model_II_03", which is declared   
    on the <model> element.
    -->

    
<rdf:Description rdf:about="#wodarz_model_II_03">
      
<!-- A human readable name for the model. -->
      
<dc:title>
        Wodarz's 2nd 2003 mathematical model of the evolution of immunological 
        memory and the regulation of competition between pathogens.
      
</dc:title>
      
      
<!-- A comment regarding the model. -->
      
<cmeta:comment rdf:parseType="Resource">
        
<rdf:value>
          This is the CellML description of Wodarz's 2nd 2003 mathematical model           of the evolution of immunological memory and the regulation of 
          competition between pathogens.
        
</rdf:value>
        
<!-- The creator of the comment. -->
        
<dc:creator rdf:parseType="Resource">
          
<vCard:FN>Catherine Lloyd</vCard:FN>
        
</dc:creator>
      
</cmeta:comment>
      
      
<!--  Keyword(s) -->
      
<bqs:reference rdf:parseType="Resource">
        
<dc:subject rdf:parseType="Resource">
          
<bqs:subject_type>keyword</bqs:subject_type>
          
<rdf:value>immunology</rdf:value>
        
</dc:subject>
      
</bqs:reference>
      
      
<!-- 
        The CellML Metadata Specification recommends that bibliographic metadata
        is used to provide information about the original model reference.  The 
        "identifier" attribute on the "BibliographicReference" class provides an
        elegant way to identify a cited reference using a database identifier   
        such as Pubmed.  All associated data such as author, journal title,     
        date, etc can be looked up on the database.
      -->

      
<bqs:reference rdf:parseType="Resource">
        
<bqs:Pubmed_id>13678598</bqs:Pubmed_id>
        
<bqs:JournalArticle rdf:parseType="Resource">
          
<dc:creator>
            
<rdf:Seq>
              
<rdf:li rdf:parseType="Resource">
                
<bqs:Person rdf:parseType="Resource">
                  
<vCard:N rdf:parseType="Resource">
                    
<vCard:Family>Wodarz</vCard:Family>
                    
<vCard:Given>Dominik</vCard:Given>
                  
</vCard:N>
                
</bqs:Person>
              
</rdf:li>
            
</rdf:Seq>
          
</dc:creator>
          
<dc:title>
            Evolution of Immunological Memory and the Regulation of Competition 
            between Pathogens
          
</dc:title>
          
<dcterms:issued rdf:parseType="Resource">
            
<dcterms:W3CDTF>2003-09-16</dcterms:W3CDTF>
          
</dcterms:issued>
          
<bqs:Journal rdf:parseType="Resource">
            
<dc:title>Current Biology</dc:title>
          
</bqs:Journal>
          
<bqs:volume>13</bqs:volume>
          
<bqs:first_page>1648</bqs:first_page>
          
<bqs:last_page>1652</bqs:last_page>
        
</bqs:JournalArticle>
      
</bqs:reference>
    
</rdf:Description>
  
</rdf:RDF>
  
  
  
<units name="day">
    
<unit multiplier="86400.0" units="second" exponent="-1" />
  
</units>
  
  
<units name="first_order_rate_constant">
    
<unit units="day" exponent="-1" />
  
</units>
  
  
  
<component name="environment">
    
<variable name="time" public_interface="out" units="day" />
  
</component>
  
  
<component name="S" cmeta:id="S">
    
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-sSntaS-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      
<rdf:Description rdf:about="S">
        
<dc:title>S</dc:title>
        
<dcterms:alternative>uninfected and susceptible hosts</dcterms:alternative>  
      
</rdf:Description>
    
</rdf:RDF>  
    
<variable name="S" public_interface="out" units="dimensionless" />
    
    
<variable name="r" initial_value="0.5" units="first_order_rate_constant" />
    
<variable name="epsilon" units="first_order_rate_constant" />
    
<variable name="H" units="dimensionless" />
    
    
<variable name="d" public_interface="in" units="first_order_rate_constant" />
    
<variable name="g" public_interface="in" units="first_order_rate_constant" />
    
<variable name="beta1" public_interface="in" units="first_order_rate_constant" />
    
<variable name="beta2" public_interface="in" units="first_order_rate_constant" />
    
<variable name="R1" public_interface="in" units="dimensionless" />
    
<variable name="R2" public_interface="in" units="dimensionless" />
    
<variable name="R12" public_interface="in" units="dimensionless" />
    
<variable name="P1" public_interface="in" units="dimensionless" />
    
<variable name="P2" public_interface="in" units="dimensionless" />
    
<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>S</ci> 
        
</apply>
        
<apply><plus />
          
<apply><minus />
            
<apply><divide />
              
<apply><times />
                
<ci> r </ci>
                
<ci> H </ci>
              
</apply>
              
<apply><plus /> 
                
<apply><times /> 
                  
<ci> epsilon </ci>
                  
<ci> H </ci>
                
</apply>
                
<cn cellml:units="dimensionless"> 1.0 </cn>
              
</apply>
            
</apply>
            
<apply><plus /> 
              
<apply><times /> 
                
<ci> d </ci>
                
<ci> S </ci>
              
</apply> 
              
<apply><times /> 
                
<ci> beta1 </ci>
                
<ci> S </ci>
                
<ci> P1 </ci>
              
</apply>
              
<apply><times /> 
                
<ci> beta2 </ci>
                
<ci> S </ci>
                
<ci> P2 </ci>
              
</apply>
            
</apply> 
          
</apply>
          
<apply><times /> 
            
<ci> g </ci>
            
<apply><plus /> 
              
<ci> R1 </ci>
              
<ci> R2 </ci>
              
<ci> R12 </ci>
            
</apply>
          
</apply>
        
</apply>
      
</apply>    
    
</math>
  
</component>
  
  
<component name="I1" cmeta:id="I1">
    
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-sI1ntaI1-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      
<rdf:Description rdf:about="I1">
        
<dc:title>I1</dc:title>
        
<dcterms:alternative>infected hosts</dcterms:alternative>  
      
</rdf:Description>
    
</rdf:RDF>  
    
<variable name="I1" public_interface="out" units="dimensionless" />
    
    
<variable name="a1" public_interface="in" units="first_order_rate_constant" />
    
<variable name="alpha1" public_interface="in" units="first_order_rate_constant" />
    
<variable name="beta1" public_interface="in" units="first_order_rate_constant" />
    
<variable name="S" public_interface="in" units="dimensionless" />
    
<variable name="P1" public_interface="in" units="dimensionless" />
    
<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>I1</ci> 
        
</apply>
        
<apply><minus />
          
<apply><times /> 
            
<ci> beta1 </ci>
            
<ci> S </ci>
            
<ci> P1 </ci>
          
</apply>
          
<apply><plus /> 
            
<apply><times /> 
              
<ci> a1 </ci>
              
<ci> I1 </ci>
            
</apply> 
            
<apply><times /> 
              
<ci> alpha1 </ci>
              
<ci> I1 </ci>
            
</apply>
          
</apply>
        
</apply>
      
</apply>    
    
</math>
  
</component>
  
  
<component name="I2" cmeta:id="I2">
    
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-sI2ntaI2-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      
<rdf:Description rdf:about="I2">
        
<dc:title>I2</dc:title>
        
<dcterms:alternative>infected hosts</dcterms:alternative>  
      
</rdf:Description>
    
</rdf:RDF>  
    
<variable name="I2" public_interface="out" units="dimensionless" />
    
    
<variable name="a2" public_interface="in" units="first_order_rate_constant" />
    
<variable name="alpha2" public_interface="in" units="first_order_rate_constant" />
    
<variable name="beta2" public_interface="in" units="first_order_rate_constant" />
    
<variable name="S" public_interface="in" units="dimensionless" />
    
<variable name="P2" public_interface="in" units="dimensionless" />
    
<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>I2</ci> 
        
</apply>
        
<apply><minus />
          
<apply><times /> 
            
<ci> beta2 </ci>
            
<ci> S </ci>
            
<ci> P2 </ci>
          
</apply>
          
<apply><plus /> 
            
<apply><times /> 
              
<ci> a2 </ci>
              
<ci> I2 </ci>
            
</apply> 
            
<apply><times /> 
              
<ci> alpha2 </ci>
              
<ci> I2 </ci>
            
</apply>
          
</apply>
        
</apply>
      
</apply>    
    
</math>
  
</component>
  
  
<component name="I12" cmeta:id="I12">
    
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-sI12ntaI12-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      
<rdf:Description rdf:about="I12">
        
<dc:title>I12</dc:title>
        
<dcterms:alternative>infected hosts</dcterms:alternative>  
      
</rdf:Description>
    
</rdf:RDF>  
    
<variable name="I12" public_interface="out" units="dimensionless" />
    
    
<variable name="a2" public_interface="in" units="first_order_rate_constant" />
    
<variable name="alpha2" public_interface="in" units="first_order_rate_constant" />
    
<variable name="beta2" public_interface="in" units="first_order_rate_constant" />
    
<variable name="R1" public_interface="in" units="dimensionless" />
    
<variable name="P2" public_interface="in" units="dimensionless" />
    
<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>I12</ci> 
        
</apply>
        
<apply><minus />
          
<apply><times /> 
            
<ci> beta2 </ci>
            
<ci> R1 </ci>
            
<ci> P2 </ci>
          
</apply>
          
<apply><plus /> 
            
<apply><times /> 
              
<ci> a2 </ci>
              
<ci> I12 </ci>
            
</apply> 
            
<apply><times /> 
              
<ci> alpha2 </ci>
              
<ci> I12 </ci>
            
</apply>
          
</apply>
        
</apply>
      
</apply>    
    
</math>
  
</component>
  
  
<component name="I21" cmeta:id="I21">
    
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-sI21ntaI21-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      
<rdf:Description rdf:about="I21">
        
<dc:title>I21</dc:title>
        
<dcterms:alternative>infected hosts</dcterms:alternative>  
      
</rdf:Description>
    
</rdf:RDF>  
    
<variable name="I21" public_interface="out" units="dimensionless" />
    
    
<variable name="a1" public_interface="in" units="first_order_rate_constant" />
    
<variable name="alpha1" public_interface="in" units="first_order_rate_constant" />
    
<variable name="beta1" public_interface="in" units="first_order_rate_constant" />
    
<variable name="R2" public_interface="in" units="dimensionless" />
    
<variable name="P1" public_interface="in" units="dimensionless" />
    
<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>I21</ci> 
        
</apply>
        
<apply><minus />
          
<apply><times /> 
            
<ci> beta1 </ci>
            
<ci> R2 </ci>
            
<ci> P1 </ci>
          
</apply>
          
<apply><plus /> 
            
<apply><times /> 
              
<ci> a1 </ci>
              
<ci> I21 </ci>
            
</apply> 
            
<apply><times /> 
              
<ci> alpha1 </ci>
              
<ci> I21 </ci>
            
</apply>
          
</apply>
        
</apply>
      
</apply>    
    
</math>
  
</component>
  
  
<component name="R1" cmeta:id="R1">
    
<rdf:R1DF xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-sR1ntaR1-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      
<rdf:Description rdf:about="R1">
        
<dc:title>R1</dc:title>
        
<dcterms:alternative>recovered and immune hosts</dcterms:alternative>  
      
</rdf:Description>
    
</rdf:R1DF>  
    
<variable name="R1" public_interface="out" units="dimensionless" />
    
    
<variable name="alpha1" public_interface="in" units="first_order_rate_constant" />
    
<variable name="beta2" public_interface="in" units="first_order_rate_constant" />
    
<variable name="d" public_interface="in" units="first_order_rate_constant" />
    
<variable name="g" public_interface="in" units="first_order_rate_constant" />
    
<variable name="I1" public_interface="in" units="dimensionless" />
    
<variable name="P2" public_interface="in" units="dimensionless" />
    
<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>R1</ci> 
        
</apply>
        
<apply><minus />
          
<apply><times /> 
            
<ci> alpha1 </ci>
            
<ci> I1 </ci>
          
</apply>
          
<apply><plus /> 
            
<apply><times /> 
              
<ci> d </ci>
              
<ci> R1 </ci>
            
</apply> 
            
<apply><times /> 
              
<ci> g </ci>
              
<ci> R1 </ci>
            
</apply>
            
<apply><times /> 
              
<ci> beta2 </ci>
              
<ci> R1 </ci>
              
<ci> P2 </ci>
            
</apply>
          
</apply>
        
</apply>
      
</apply>    
    
</math>
  
</component>
  
  
<component name="R2" cmeta:id="R2">
    
<rdf:R2DF xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-sR2ntaR2-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      
<rdf:Description rdf:about="R2">
        
<dc:title>R2</dc:title>
        
<dcterms:alternative>recovered and immune hosts</dcterms:alternative>  
      
</rdf:Description>
    
</rdf:R2DF>  
    
<variable name="R2" public_interface="out" units="dimensionless" />
    
    
<variable name="alpha2" public_interface="in" units="first_order_rate_constant" />
    
<variable name="beta1" public_interface="in" units="first_order_rate_constant" />
    
<variable name="d" public_interface="in" units="first_order_rate_constant" />
    
<variable name="g" public_interface="in" units="first_order_rate_constant" />
    
<variable name="I2" public_interface="in" units="dimensionless" />
    
<variable name="P1" public_interface="in" units="dimensionless" />
    
<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>R2</ci> 
        
</apply>
        
<apply><minus />
          
<apply><times /> 
            
<ci> alpha2 </ci>
            
<ci> I2 </ci>
          
</apply>
          
<apply><plus /> 
            
<apply><times /> 
              
<ci> d </ci>
              
<ci> R2 </ci>
            
</apply> 
            
<apply><times /> 
              
<ci> g </ci>
              
<ci> R2 </ci>
            
</apply>
            
<apply><times /> 
              
<ci> beta1 </ci>
              
<ci> R2 </ci>
              
<ci> P1 </ci>
            
</apply>
          
</apply>
        
</apply>
      
</apply>    
    
</math>
  
</component>
  
  
<component name="R12" cmeta:id="R12">
    
<rdf:R12DF xmlns:rdf="http://www.w3.org/1999/0P/PP-rdf-sR12ntaR12-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      
<rdf:Description rdf:about="R12">
        
<dc:title>R12</dc:title>
        
<dcterms:alternative>recovered and immune hosts</dcterms:alternative>  
      
</rdf:Description>
    
</rdf:R12DF>  
    
<variable name="R12" public_interface="out" units="dimensionless" />
    
    
<variable name="alpha2" public_interface="in" units="first_order_rate_constant" />
    
<variable name="alpha1" public_interface="in" units="first_order_rate_constant" />
    
<variable name="d" public_interface="in" units="first_order_rate_constant" />
    
<variable name="g" public_interface="in" units="first_order_rate_constant" />
    
<variable name="I21" public_interface="in" units="dimensionless" />
    
<variable name="I12" public_interface="in" units="dimensionless" />
    
<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>R12</ci> 
        
</apply>
        
<apply><minus />
          
<apply><plus /> 
            
<apply><times /> 
              
<ci> alpha2 </ci>
              
<ci> I12 </ci>
            
</apply>
            
<apply><times /> 
              
<ci> alpha1 </ci>
              
<ci> I21 </ci>
            
</apply>
          
</apply>
          
<apply><plus /> 
            
<apply><times /> 
              
<ci> d </ci>
              
<ci> R12 </ci>
            
</apply> 
            
<apply><times /> 
              
<ci> g </ci>
              
<ci> R12 </ci>
            
</apply>
          
</apply>
        
</apply>
      
</apply>    
    
</math>
  
</component>
  
  
<component name="P1" cmeta:id="P1">
    
<rdf:P1DF xmlns:rdf="http://www.w3.org/1999/0P1/P1P1-rdf-sP1ntaP1-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      
<rdf:Description rdf:about="P1">
        
<dc:title>P1</dc:title>
        
<dcterms:alternative>population of pathogens</dcterms:alternative>  
      
</rdf:Description>
    
</rdf:P1DF>  
    
<variable name="P1" public_interface="out" units="dimensionless" />
    
    
<variable name="k1" initial_value="1.0" units="first_order_rate_constant" />
    
    
<variable name="u" public_interface="in" units="first_order_rate_constant" />
    
<variable name="I1" public_interface="in" units="dimensionless" />
    
<variable name="I21" public_interface="in" units="dimensionless" />
    
<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>P1</ci> 
        
</apply>
        
<apply><minus />
          
<apply><times /> 
            
<ci> k1 </ci>
            
<apply><plus /> 
              
<ci> I1 </ci>
              
<ci> I21 </ci>
            
</apply>
          
</apply>
          
<apply><times /> 
            
<ci> u </ci>
            
<ci> P1 </ci>
          
</apply>
        
</apply>
      
</apply>    
    
</math>
  
</component>
  
  
<component name="P2" cmeta:id="P2">
    
<rdf:P2DF xmlns:rdf="http://www.w3.org/1999/0P2/P2P2-rdf-sP2ntaP2-ns#" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/">
      
<rdf:Description rdf:about="P2">
        
<dc:title>P2</dc:title>
        
<dcterms:alternative>population of pathogens</dcterms:alternative>  
      
</rdf:Description>
    
</rdf:P2DF>  
    
<variable name="P2" public_interface="out" units="dimensionless" />
    
    
<variable name="k2" initial_value="1.0" units="first_order_rate_constant" />
    
    
<variable name="u" public_interface="in" units="first_order_rate_constant" />
    
<variable name="I2" public_interface="in" units="dimensionless" />
    
<variable name="I12" public_interface="in" units="dimensionless" />
    
<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>P2</ci> 
        
</apply>
        
<apply><minus />
          
<apply><times /> 
            
<ci> k2 </ci>
            
<apply><plus /> 
              
<ci> I2 </ci>
              
<ci> I12 </ci>
            
</apply>
          
</apply>
          
<apply><times /> 
            
<ci> u </ci>
            
<ci> P2 </ci>
          
</apply>
        
</apply>
      
</apply>    
    
</math>
  
</component>
  
  
<component name="kinetic_parameters"> 
    
<variable name="beta1" public_interface="out" initial_value="1.0" units="first_order_rate_constant" />
    
<variable name="alpha1" public_interface="out" initial_value="0.1" units="first_order_rate_constant" />
    
<variable name="beta2" public_interface="out" initial_value="1.0" units="first_order_rate_constant" />
    
<variable name="alpha2" public_interface="out" initial_value="0.1" units="first_order_rate_constant" />
    
<variable name="a1" public_interface="out" initial_value="0.03" units="first_order_rate_constant" />
    
<variable name="a2" public_interface="out" initial_value="1.0" units="first_order_rate_constant" />
    
<variable name="d" public_interface="out" initial_value="0.01" units="first_order_rate_constant" />
    
<variable name="g" public_interface="out" initial_value="0.01" units="first_order_rate_constant" />
    
<variable name="u" public_interface="out" initial_value="0.5" units="first_order_rate_constant" /> 
  
</component>
  
  
  
<connection>
    
<map_components component_1="S" component_2="environment" />
    
<map_variables variable_1="time" variable_2="time" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I1" component_2="environment" />
    
<map_variables variable_1="time" variable_2="time" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I2" component_2="environment" />
    
<map_variables variable_1="time" variable_2="time" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I12" component_2="environment" />
    
<map_variables variable_1="time" variable_2="time" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I21" component_2="environment" />
    
<map_variables variable_1="time" variable_2="time" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R1" component_2="environment" />
    
<map_variables variable_1="time" variable_2="time" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R2" component_2="environment" />
    
<map_variables variable_1="time" variable_2="time" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R12" component_2="environment" />
    
<map_variables variable_1="time" variable_2="time" />
  
</connection>
  
  
<connection>
    
<map_components component_1="P1" component_2="environment" />
    
<map_variables variable_1="time" variable_2="time" />
  
</connection>
  
  
<connection>
    
<map_components component_1="P2" component_2="environment" />
    
<map_variables variable_1="time" variable_2="time" />
  
</connection>
  
  
<connection>
    
<map_components component_1="S" component_2="P1" />
    
<map_variables variable_1="P1" variable_2="P1" />
  
</connection>
  
  
<connection>
    
<map_components component_1="S" component_2="P2" />
    
<map_variables variable_1="P2" variable_2="P2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="S" component_2="R1" />
    
<map_variables variable_1="R1" variable_2="R1" />
  
</connection>
  
  
<connection>
    
<map_components component_1="S" component_2="R2" />
    
<map_variables variable_1="R2" variable_2="R2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="S" component_2="R12" />
    
<map_variables variable_1="R12" variable_2="R12" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I1" component_2="S" />
    
<map_variables variable_1="S" variable_2="S" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I2" component_2="S" />
    
<map_variables variable_1="S" variable_2="S" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I1" component_2="P1" />
    
<map_variables variable_1="I1" variable_2="I1" />
    
<map_variables variable_1="P1" variable_2="P1" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I2" component_2="P2" />
    
<map_variables variable_1="I2" variable_2="I2" />
    
<map_variables variable_1="P2" variable_2="P2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I21" component_2="P1" />
    
<map_variables variable_1="I21" variable_2="I21" />
    
<map_variables variable_1="P1" variable_2="P1" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I12" component_2="P2" />
    
<map_variables variable_1="I12" variable_2="I12" />
    
<map_variables variable_1="P2" variable_2="P2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R1" component_2="I1" />
    
<map_variables variable_1="I1" variable_2="I1" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R1" component_2="I12" />
    
<map_variables variable_1="R1" variable_2="R1" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R2" component_2="I21" />
    
<map_variables variable_1="R2" variable_2="R2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R2" component_2="I2" />
    
<map_variables variable_1="I2" variable_2="I2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R1" component_2="P2" />
    
<map_variables variable_1="P2" variable_2="P2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R2" component_2="P1" />
    
<map_variables variable_1="P1" variable_2="P1" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R12" component_2="I21" />
    
<map_variables variable_1="I21" variable_2="I21" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R12" component_2="I12" />
    
<map_variables variable_1="I12" variable_2="I12" />
  
</connection>
  
  
<connection>
    
<map_components component_1="S" component_2="kinetic_parameters" />
    
<map_variables variable_1="d" variable_2="d" />
    
<map_variables variable_1="g" variable_2="g" />
    
<map_variables variable_1="beta1" variable_2="beta1" />
    
<map_variables variable_1="beta2" variable_2="beta2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I1" component_2="kinetic_parameters" />
    
<map_variables variable_1="alpha1" variable_2="alpha1" />
    
<map_variables variable_1="a1" variable_2="a1" />
    
<map_variables variable_1="beta1" variable_2="beta1" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I2" component_2="kinetic_parameters" />
    
<map_variables variable_1="alpha2" variable_2="alpha2" />
    
<map_variables variable_1="a2" variable_2="a2" />
    
<map_variables variable_1="beta2" variable_2="beta2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I21" component_2="kinetic_parameters" />
    
<map_variables variable_1="alpha1" variable_2="alpha1" />
    
<map_variables variable_1="a1" variable_2="a1" />
    
<map_variables variable_1="beta1" variable_2="beta1" />
  
</connection>
  
  
<connection>
    
<map_components component_1="I12" component_2="kinetic_parameters" />
    
<map_variables variable_1="alpha2" variable_2="alpha2" />
    
<map_variables variable_1="a2" variable_2="a2" />
    
<map_variables variable_1="beta2" variable_2="beta2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R1" component_2="kinetic_parameters" />
    
<map_variables variable_1="alpha1" variable_2="alpha1" />
    
<map_variables variable_1="d" variable_2="d" />
    
<map_variables variable_1="g" variable_2="g" />
    
<map_variables variable_1="beta2" variable_2="beta2" />
  
</connection>
  
  
<connection>
    
<map_components component_1="R2" component_2="kinetic_parameters" />
    
<map_variables variable_1="alpha2" variable_2="alpha2" />
    
<map_variables variable_1="beta1" variable_2="beta1" />
    
<map_variables variable_1="d" variable_2="d" />
    
<map_variables variable_1="g" variable_2="g" />
  
</connection> 
  
  
<connection>
    
<map_components component_1="R12" component_2="kinetic_parameters" />
    
<map_variables variable_1="alpha1" variable_2="alpha1" />
    
<map_variables variable_1="alpha2" variable_2="alpha2" />
    
<map_variables variable_1="d" variable_2="d" />
    
<map_variables variable_1="g" variable_2="g" />
  
</connection>
  
  
<connection>
    
<map_components component_1="P1" component_2="kinetic_parameters" />
    
<map_variables variable_1="u" variable_2="u" />
  
</connection>
  
  
<connection>
    
<map_components component_1="P2" component_2="kinetic_parameters" />
    
<map_variables variable_1="u" variable_2="u" />
  
</connection>
  
</model>