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     <p>The paper describes a model of tumor control via alternating immunostimulating and immunosuppressive phases. 
Created by COPASI 4.25 (Build 207) 

This model is described in the article: 
In silico tumor control induced via alternating immunostimulating and immunosuppressive phases
AI Reppas, JCL Alfonso, and H Hatzikirou
Virulence 7:2, 174--186

Abstract: 
Despite recent advances in the field of Oncoimmunology, the success potential of immunomodulatory therapies against cancer remains to be elucidated. One of the reasons is the lack of understanding on the complex interplay between tumor growth dynamics and the associated immune system responses. Toward this goal, we consider a mathematical model of vascularized tumor growth and the corresponding effector cell recruitment dynamics. Bifurcation analysis allows for the exploration of model’s dynamic behavior and the determination of these parameter regimes that result in immune-mediated tumor control. In this work, we focus on a particular tumor evasion regime that involves tumor and effector cell concentration oscillations of slowly increasing and decreasing amplitude, respectively. Considering a temporal multiscale analysis, we derive an analytically tractable mapping of model solutions onto a weakly negatively damped harmonic oscillator. Based on our analysis, we propose a theory-driven intervention strategy involving immunostimulating and immunosuppressive phases to induce long-term tumor control.

To cite BioModels Database, please use: BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models . 
To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. 
Please refer to CC0 Public Domain Dedication for more information.</p>
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            </species>
      <species boundaryCondition="true" compartment="tumor_microenvironment" constant="false" hasOnlySubstanceUnits="false" id="f" initialConcentration="0.414213562373095" metaid="COPASI4" name="f" substanceUnits="substance">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>phenomenological scaling function f(R,B)</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI4">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/ncit/C54025"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI4">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T11:03:58Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:ncit:C54025"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </species>
      <species boundaryCondition="true" compartment="tumor_microenvironment" constant="false" hasOnlySubstanceUnits="false" id="E_0" initialConcentration="10" metaid="COPASI5" name="E'" substanceUnits="substance">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>effector cell count/1e5

easier for plotting</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI5">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/ncit/C28241"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI5">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T12:36:57Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:ncit:C28241"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </species>
    </listOfSpecies>
    <listOfParameters>
      <parameter constant="true" id="B" metaid="COPASI6" name="B" units="unit_0" value="0.5">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>vascularization parameter, 0.40/0.50/0.65/0.80/0.95</pre>
          </body>
        </notes>
        <annotation>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI6">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T11:04:02Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="lm" metaid="COPASI7" name="lm" units="unit_1" value="1.34">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>Mitotic rate of tumor cells</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI7">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000610"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI7">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T12:39:35Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000610"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="la" metaid="COPASI8" name="la" units="unit_1" value="0.14">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>Death rate of tumor cells</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI8">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/ncit/C53346"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI8">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T12:39:36Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:ncit:C53346"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="ld" metaid="COPASI9" name="ld" units="unit_0" value="0.3">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>Characteristic nutrient diffusion length, mm
0.2-0.3</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI9">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000466"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI9">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T12:39:38Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000466"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="c" metaid="COPASI10" name="c" units="unit_1" value="0.03">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>Killing rate of tumor cells by effectors</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI10">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/ncit/C53346"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI10">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T12:39:39Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:ncit:C53346"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="k" metaid="COPASI11" name="k" units="unit_0" value="2.72">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>Tumor volume where effector recruitment rate is half-maximal</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI11">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000193"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI11">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T12:39:40Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000193"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="d1" metaid="COPASI12" name="d1" units="unit_1" value="0.01">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>Inactivation rate of effectors by tumor cells</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI12">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/ncit/C53346"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI12">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T12:39:41Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:ncit:C53346"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="d0" metaid="COPASI13" name="d0" units="unit_1" value="0.37">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>Death rate of effectors</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI13">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/ncit/C53346"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI13">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T12:39:43Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:ncit:C53346"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="sigma" metaid="COPASI14" name="sigma" units="unit_1" value="13000">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>Background rate of effector recruitment</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI14">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000610"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI14">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T12:39:46Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000610"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
      <parameter constant="true" id="r" metaid="COPASI15" name="r" units="unit_1" value="0.57">
        <notes>
          <body xmlns="http://www.w3.org/1999/xhtml">
            <pre>immune recruitment rate, 0.54/0.57/0.60</pre>
          </body>
        </notes>
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI15">
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000610"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI15">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T12:40:18Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000610"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
            </parameter>
    </listOfParameters>
    <listOfRules>
      <assignmentRule variable="E_0">
        <math xmlns="http://www.w3.org/1998/Math/MathML">        
          <apply>
            <divide/>
            <ci> E </ci>
            <cn> 100000 </cn>
          </apply>
        </math>
            </assignmentRule>
      <assignmentRule variable="f">
        <math xmlns="http://www.w3.org/1998/Math/MathML">        
          <apply>
            <divide/>
            <apply>
              <power/>
              <ci> R </ci>
              <apply>
                <minus/>
                <ci> B </ci>
                <cn> 1 </cn>
              </apply>
            </apply>
            <apply>
              <plus/>
              <apply>
                <power/>
                <ci> R </ci>
                <apply>
                  <minus/>
                  <ci> B </ci>
                  <cn> 1 </cn>
                </apply>
              </apply>
              <cn> 1 </cn>
            </apply>
          </apply>
        </math>
            </assignmentRule>
    </listOfRules>
    <listOfReactions>
      <reaction fast="false" id="tumor_growth" metaid="COPASI16" name="tumor growth" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI16">
              <bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0008283"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000393"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI16">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T13:03:53Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0008283"/>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000393"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfProducts>
          <speciesReference constant="true" species="R" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> tumor_microenvironment </ci>
              <apply>
                <ci> tumor_growth_0 </ci>
                <ci> lm </ci>
                <ci> B </ci>
                <ci> R </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction fast="false" id="tumor_death" metaid="COPASI17" name="tumor death" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI17">
              <bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000179"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0008219"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI17">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T13:03:57Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0008219"/>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000179"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfReactants>
          <speciesReference constant="true" species="R" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> tumor_microenvironment </ci>
              <apply>
                <ci> tumor_death_0 </ci>
                <ci> la </ci>
                <ci> R </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction fast="false" id="tumor_killing" metaid="COPASI18" name="tumor killing" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI18">
              <bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000179"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0001909"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI18">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T13:03:59Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0001909"/>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000179"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfReactants>
          <speciesReference constant="true" species="R" stoichiometry="1"/>
        </listOfReactants>
        <listOfModifiers>
          <modifierSpeciesReference species="E_0"/>
          <modifierSpeciesReference species="f"/>
        </listOfModifiers>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> tumor_microenvironment </ci>
              <apply>
                <ci> killing </ci>
                <ci> c </ci>
                <ci> E_0 </ci>
                <ci> R </ci>
                <ci> f </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction fast="false" id="tumor_nutrient_supply" metaid="COPASI19" name="tumor nutrient supply" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI19">
              <bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0008283"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000393"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI19">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T13:04:23Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0008283"/>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000393"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfProducts>
          <speciesReference constant="true" species="R" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> tumor_microenvironment </ci>
              <apply>
                <ci> nutrience </ci>
                <ci> lm </ci>
                <ci> B </ci>
                <ci> ld </ci>
                <ci> R </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction fast="false" id="effector_stimulation" metaid="COPASI20" name="effector stimulation" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI20">
              <bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000393"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0070661"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI20">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T13:04:34Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0070661"/>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000393"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfProducts>
          <speciesReference constant="true" species="E" stoichiometry="1"/>
        </listOfProducts>
        <listOfModifiers>
          <modifierSpeciesReference species="R"/>
        </listOfModifiers>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> tumor_microenvironment </ci>
              <apply>
                <ci> stimulation </ci>
                <ci> r </ci>
                <ci> R </ci>
                <ci> E </ci>
                <ci> k </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction fast="false" id="effector_exhaustion" metaid="COPASI21" name="effector exhaustion" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI21">
              <bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0008219"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000179"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI21">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T13:04:49Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0008219"/>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000179"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfReactants>
          <speciesReference constant="true" species="E" stoichiometry="1"/>
        </listOfReactants>
        <listOfModifiers>
          <modifierSpeciesReference species="R"/>
          <modifierSpeciesReference species="f"/>
        </listOfModifiers>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> tumor_microenvironment </ci>
              <apply>
                <ci> effector_exhaustion_0 </ci>
                <ci> d1 </ci>
                <ci> E </ci>
                <ci> R </ci>
                <ci> f </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction fast="false" id="effector_death" metaid="COPASI22" name="effector death" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI22">
              <bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0008219"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000179"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI22">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T13:04:57Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0008219"/>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000179"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfReactants>
          <speciesReference constant="true" species="E" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> tumor_microenvironment </ci>
              <ci> d0 </ci>
              <ci> E </ci>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction fast="false" id="effector_source" metaid="COPASI23" name="effector source" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI23">
              <bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000393"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0070661"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI23">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T13:05:02Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0070661"/>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000393"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfProducts>
          <speciesReference constant="true" species="E" stoichiometry="1"/>
        </listOfProducts>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> tumor_microenvironment </ci>
              <apply>
                <ci> Constant_flux__irreversible </ci>
                <ci> sigma </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
      <reaction fast="false" id="tumor_nutrient_missuply" metaid="COPASI24" name="tumor nutrient missuply" reversible="false">
        <annotation>
          <rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" xmlns:vCard4="http://www.w3.org/2006/vcard/ns#" xmlns:bqbiol="http://biomodels.net/biology-qualifiers/" xmlns:bqmodel="http://biomodels.net/model-qualifiers/">
            <rdf:Description rdf:about="#COPASI24">
              <bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/sbo/SBO:0000179"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	
	<bqbiol:isVersionOf>
	<rdf:Bag>
	<rdf:li rdf:resource="http://identifiers.org/go/GO:0008219"/>
	</rdf:Bag>
	</bqbiol:isVersionOf>
	</rdf:Description>
	
	
          </rdf:RDF>
          <COPASI xmlns="http://www.copasi.org/static/sbml">
            <rdf:RDF xmlns:CopasiMT="http://www.copasi.org/RDF/MiriamTerms#" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
              <rdf:Description rdf:about="#COPASI24">
                <dcterms:created>
                  <rdf:Description>
                    <dcterms:W3CDTF>2019-07-11T13:32:16Z</dcterms:W3CDTF>
                  </rdf:Description>
                </dcterms:created>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:go:GO:0008219"/>
                <CopasiMT:isVersionOf rdf:resource="urn:miriam:sbo:SBO:0000179"/>
              </rdf:Description>
            </rdf:RDF>
          </COPASI>
        </annotation>
              <listOfReactants>
          <speciesReference constant="true" species="R" stoichiometry="1"/>
        </listOfReactants>
        <kineticLaw>
          <math xmlns="http://www.w3.org/1998/Math/MathML">          
            <apply>
              <times/>
              <ci> tumor_microenvironment </ci>
              <apply>
                <ci> nutrience_0 </ci>
                <ci> lm </ci>
                <ci> B </ci>
                <ci> ld </ci>
                <ci> R </ci>
              </apply>
            </apply>
          </math>
                </kineticLaw>
      </reaction>
    </listOfReactions>
  </model>
</sbml>