<?xml version="1.0" encoding="utf-8"?>
<model 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:dcterms="http://purl.org/dc/terms/" xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" name="wodarz_2003" cmeta:id="wodarz_2003" 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#">
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modelling the Evolution of Immunological Memory</title>
<author>
<firstname>Catherine</firstname>
<surname>Lloyd</surname>
<affiliation>
<shortaffil>Auckland Bioengineering Institute, The University of Auckland</shortaffil>
</affiliation>
</author>
</articleinfo>
<section id="sec_status">
<title>Model Status</title>
<para>
This model runs in Open Cell but due to the timescale being in days it is not able to be easily graphed in COR. The model can produce output that matches figure 2A in the published paper. The units have been checked and they balance.
</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>
ABSTRACT: Memory is a central characteristic of immune responses. It is defined as an elevated number of specific immune cells that remain after resolution of infection and can protect the host against reinfection. The evolution of immunological memory is subject to debate. The advantages of memory discussed so far include protection from reinfection, control of chronic infection, and the transfer of immune function to the next generation. Mathematical models are used to identify a new force that can drive the evolution of immunological memory: the duration of memory can regulate the degree of competition between different pathogens. While a long duration of memory provides lasting protection against reinfection, it may also allow an inferior pathogen species to persist. This can be detrimental for the host if the inferior pathogen is more virulent. On the other hand, a shorter duration of memory ensures that an inferior pathogen species is excluded. This can be beneficial for the host if the inferior pathogen is more virulent. Thus, while in the absence of pathogen diversity memory is always expected to evolve to a long duration, under specific circumstances, memory can evolve toward shorter durations in the presence of pathogen diversity.
</para>
<para>
The original paper reference is cited below:
</para>
<para>
Evolution of Immunological Memory and the Regulation of Competition between Pathogens, Dominik Wodarz, 2003, <emphasis>Current Biology</emphasis>, 13, 1648-1652. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/13678598">PubMed ID: 13678598</ulink>
</para>
<informalfigure float="0" id="fig_cell_diagram1">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram1</title>
</objectinfo>
<imagedata fileref="wodarz_2003a.png"/>
</imageobject>
</mediaobject>
<caption>Interactions between a single pathogen population and a host population.</caption>
</informalfigure>
<informalfigure float="0" id="fig_cell_diagram2">
<mediaobject>
<imageobject>
<objectinfo>
<title>cell diagram2</title>
</objectinfo>
<imagedata fileref="wodarz_2003b.png"/>
</imageobject>
</mediaobject>
<caption>Interactions between two pathogen populations and a host population.</caption>
</informalfigure>
</sect1>
</article>
</documentation>
<rdf:RDF>
<rdf:Description rdf:about="#S">
<dc:title>S</dc:title>
<dcterms:alternative>uninfected and susceptible hosts</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I1">
<dc:title>I1</dc:title>
<dcterms:alternative>infected hosts</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I2">
<dc:title>I2</dc:title>
<dcterms:alternative>infected hosts</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I12">
<dc:title>I12</dc:title>
<dcterms:alternative>infected hosts</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#I21">
<dc:title>I21</dc:title>
<dcterms:alternative>infected hosts</dcterms:alternative>
</rdf:Description>
</rdf:RDF>
<rdf:R1DF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#R1">
<dc:title>R1</dc:title>
<dcterms:alternative>recovered and immune hosts</dcterms:alternative>
</rdf:Description>
</rdf:R1DF>
<rdf:R2DF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#R2">
<dc:title>R2</dc:title>
<dcterms:alternative>recovered and immune hosts</dcterms:alternative>
</rdf:Description>
</rdf:R2DF>
<rdf:R12DF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#R12">
<dc:title>R12</dc:title>
<dcterms:alternative>recovered and immune hosts</dcterms:alternative>
</rdf:Description>
</rdf:R12DF>
<rdf:P1DF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#P1">
<dc:title>P1</dc:title>
<dcterms:alternative>population of pathogens</dcterms:alternative>
</rdf:Description>
</rdf:P1DF>
<rdf:P2DF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="#P2">
<dc:title>P2</dc:title>
<dcterms:alternative>population of pathogens</dcterms:alternative>
</rdf:Description>
</rdf:P2DF>
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Seq rdf:about="rdf:#citationAuthorsSeq">
<rdf:li rdf:resource="rdf:#author1Vcard"/>
</rdf:Seq>
<rdf:Description rdf:about="rdf:#c719dd67-0bf3-441e-8dcc-9bd7be04bf67">
<vCard:ORG rdf:resource="rdf:#4c5a7ebe-9bfa-4ffd-aa26-3939043c4175"/>
<vCard:EMAIL rdf:resource="rdf:#7994b0f0-d145-482c-860c-7e20a57ae564"/>
<vCard:N rdf:resource="rdf:#0cd404ed-f8a6-4537-9ff9-f4d1cf378fe9"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#0cd404ed-f8a6-4537-9ff9-f4d1cf378fe9">
<vCard:Given>Catherine</vCard:Given>
<vCard:Family>Lloyd</vCard:Family>
<vCard:Other>May</vCard:Other>
</rdf:Description>
<rdf:Description rdf:about="#wodarz_2003">
<dc:title>
Wodarz's 2nd 2003 mathematical model of the evolution of immunological
memory and the regulation of competition between pathogens.
</dc:title>
<cmeta:comment xmlns:cmeta="http://www.cellml.org/metadata/1.0#" rdf:resource="rdf:#ac74765f-535e-48f3-9de6-4ae538fbec5c"/>
<bqs:reference rdf:resource="rdf:#c2ffd07b-2fd1-41b0-bc90-b086171bc24c"/>
<bqs:reference rdf:resource="rdf:#e5516720-c1e2-4ae2-bbe6-925204067934"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#8194e217-9709-4ea3-8220-045c3ec7b106">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>immunology</rdf:li>
<rdf:li>interspecific pathogenic competition</rdf:li>
</rdf:Bag>
</rdf:value>
</rdf:Description>
<rdf:Description rdf:about="">
<dc:publisher>
The University of Auckland, Bioengineering Institute
</dc:publisher>
<dcterms:created rdf:resource="rdf:#ac4ccc76-4569-48be-8324-7c378243f2cf"/>
<dc:creator rdf:resource="rdf:#c719dd67-0bf3-441e-8dcc-9bd7be04bf67"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ac74765f-535e-48f3-9de6-4ae538fbec5c">
<dc:creator rdf:resource="rdf:#9025aa44-9e18-4f72-929a-c86b0e27f9fa"/>
<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>
</rdf:Description>
<rdf:Description rdf:about="rdf:#34be0937-46e5-4c7f-bf21-cf0d501445be">
<dcterms:W3CDTF>2003-09-16</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1Vcard">
<rdf:type rdf:resource="http://www.cellml.org/bqs/1.0#Person"/>
<vCard:N rdf:resource="rdf:#author1VcardN"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#f39648d7-22c1-44ff-8cd1-615f9026e25c">
<dc:creator rdf:resource="rdf:#citationAuthorsSeq"/>
<dc:title>Evolution of Immunological Memory and the Regulation of Competition between Pathogens</dc:title>
<bqs:volume>13</bqs:volume>
<bqs:first_page>1648</bqs:first_page>
<bqs:Journal rdf:resource="rdf:#4d81b96d-ac9a-4c9e-b606-53bf6a3e2bec"/>
<dcterms:issued rdf:resource="rdf:#34be0937-46e5-4c7f-bf21-cf0d501445be"/>
<bqs:last_page>1652</bqs:last_page>
</rdf:Description>
<rdf:Description rdf:about="rdf:#4c5a7ebe-9bfa-4ffd-aa26-3939043c4175">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>The Bioengineering Institute</vCard:Orgunit>
</rdf:Description>
<rdf:Description rdf:about="rdf:#9025aa44-9e18-4f72-929a-c86b0e27f9fa">
<vCard:FN>Catherine Lloyd</vCard:FN>
</rdf:Description>
<rdf:Description rdf:about="rdf:#author1VcardN">
<vCard:Given>Dominik</vCard:Given>
<vCard:Family>Wodarz</vCard:Family>
</rdf:Description>
<rdf:Description rdf:about="rdf:#ac4ccc76-4569-48be-8324-7c378243f2cf">
<dcterms:W3CDTF>2003-12-17</dcterms:W3CDTF>
</rdf:Description>
<rdf:Description rdf:about="rdf:#e5516720-c1e2-4ae2-bbe6-925204067934">
<bqs:Pubmed_id>13678598</bqs:Pubmed_id>
<bqs:JournalArticle rdf:resource="rdf:#f39648d7-22c1-44ff-8cd1-615f9026e25c"/>
</rdf:Description>
<rdf:Description rdf:about="rdf:#7994b0f0-d145-482c-860c-7e20a57ae564">
<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:#4d81b96d-ac9a-4c9e-b606-53bf6a3e2bec">
<dc:title>Current Biology</dc:title>
</rdf:Description>
<rdf:Description rdf:about="rdf:#c2ffd07b-2fd1-41b0-bc90-b086171bc24c">
<dc:subject rdf:resource="rdf:#8194e217-9709-4ea3-8220-045c3ec7b106"/>
</rdf:Description>
</rdf:RDF> <units xmlns="http://www.cellml.org/cellml/1.0#" name="day">
<unit units="second" multiplier="86400"/>
</units>
<units xmlns="http://www.cellml.org/cellml/1.0#" name="first_order_rate_constant">
<unit units="day" exponent="-1"/>
</units>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="environment">
<variable name="time" units="day" public_interface="out"/>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="S">
<variable name="S" units="dimensionless" initial_value="100" public_interface="out"/>
<variable name="r" units="first_order_rate_constant" initial_value="0.5"/>
<variable name="epsilon" units="dimensionless" initial_value="0.1"/>
<variable name="H" units="dimensionless"/>
<variable name="d" units="first_order_rate_constant" public_interface="in"/>
<variable name="g" units="first_order_rate_constant" public_interface="in"/>
<variable name="beta_1" units="first_order_rate_constant" public_interface="in"/>
<variable name="beta_2" units="first_order_rate_constant" public_interface="in"/>
<variable name="R_1" units="dimensionless" public_interface="in"/>
<variable name="R_2" units="dimensionless" public_interface="in"/>
<variable name="R_12" units="dimensionless" public_interface="in"/>
<variable name="P_1" units="dimensionless" public_interface="in"/>
<variable name="P_2" units="dimensionless" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<variable name="I_1" units="dimensionless" public_interface="in"/>
<variable name="I_2" units="dimensionless" public_interface="in"/>
<variable name="I_12" units="dimensionless" public_interface="in"/>
<variable name="I_21" units="dimensionless" public_interface="in"/>
<variable name="P" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>P</ci>
<apply>
<plus/>
<ci>P_1</ci>
<ci>P_2</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>H</ci>
<apply>
<plus/>
<ci>S</ci>
<ci>I_1</ci>
<ci>R_1</ci>
<ci>I_2</ci>
<ci>R_2</ci>
<ci>I_12</ci>
<ci>I_21</ci>
<ci>R_12</ci>
</apply>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>S</ci>
</apply>
<apply>
<plus/>
<apply>
<minus/>
<apply>
<minus/>
<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</cn>
</apply>
</apply>
<apply>
<times/>
<ci>d</ci>
<ci>S</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_1</ci>
<ci>S</ci>
<ci>P_1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_2</ci>
<ci>S</ci>
<ci>P_2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>g</ci>
<apply>
<plus/>
<ci>R_1</ci>
<ci>R_2</ci>
<ci>R_12</ci>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="I1">
<variable name="I_1" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="a_1" units="first_order_rate_constant" public_interface="in"/>
<variable name="alpha_1" units="first_order_rate_constant" public_interface="in"/>
<variable name="beta_1" units="first_order_rate_constant" public_interface="in"/>
<variable name="S" units="dimensionless" public_interface="in"/>
<variable name="P_1" units="dimensionless" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>I_1</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>beta_1</ci>
<ci>S</ci>
<ci>P_1</ci>
</apply>
<apply>
<times/>
<ci>a_1</ci>
<ci>I_1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>alpha_1</ci>
<ci>I_1</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="I2">
<variable name="I_2" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="a_2" units="first_order_rate_constant" public_interface="in"/>
<variable name="alpha_2" units="first_order_rate_constant" public_interface="in"/>
<variable name="beta_2" units="first_order_rate_constant" public_interface="in"/>
<variable name="S" units="dimensionless" public_interface="in"/>
<variable name="P_2" units="dimensionless" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>I_2</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>beta_2</ci>
<ci>S</ci>
<ci>P_2</ci>
</apply>
<apply>
<times/>
<ci>a_2</ci>
<ci>I_2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>alpha_2</ci>
<ci>I_2</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="I12">
<variable name="I_12" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="a_2" units="first_order_rate_constant" public_interface="in"/>
<variable name="alpha_2" units="first_order_rate_constant" public_interface="in"/>
<variable name="beta_2" units="first_order_rate_constant" public_interface="in"/>
<variable name="R_1" units="dimensionless" public_interface="in"/>
<variable name="P_2" units="dimensionless" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>I_12</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>beta_2</ci>
<ci>R_1</ci>
<ci>P_2</ci>
</apply>
<apply>
<times/>
<ci>a_2</ci>
<ci>I_12</ci>
</apply>
</apply>
<apply>
<times/>
<ci>alpha_2</ci>
<ci>I_12</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="I21">
<variable name="I_21" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="a_1" units="first_order_rate_constant" public_interface="in"/>
<variable name="alpha_1" units="first_order_rate_constant" public_interface="in"/>
<variable name="beta_1" units="first_order_rate_constant" public_interface="in"/>
<variable name="R_2" units="dimensionless" public_interface="in"/>
<variable name="P_1" units="dimensionless" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>I_21</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>beta_1</ci>
<ci>R_2</ci>
<ci>P_1</ci>
</apply>
<apply>
<times/>
<ci>a_1</ci>
<ci>I_21</ci>
</apply>
</apply>
<apply>
<times/>
<ci>alpha_1</ci>
<ci>I_21</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="R1">
<variable name="R_1" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="alpha_1" units="first_order_rate_constant" public_interface="in"/>
<variable name="beta_2" units="first_order_rate_constant" public_interface="in"/>
<variable name="d" units="first_order_rate_constant" public_interface="in"/>
<variable name="g" units="first_order_rate_constant" public_interface="in"/>
<variable name="I_1" units="dimensionless" public_interface="in"/>
<variable name="P_2" units="dimensionless" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>R_1</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_1</ci>
<ci>I_1</ci>
</apply>
<apply>
<times/>
<ci>d</ci>
<ci>R_1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>g</ci>
<ci>R_1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_2</ci>
<ci>R_1</ci>
<ci>P_2</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="R2">
<variable name="R_2" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="alpha_2" units="first_order_rate_constant" public_interface="in"/>
<variable name="beta_1" units="first_order_rate_constant" public_interface="in"/>
<variable name="d" units="first_order_rate_constant" public_interface="in"/>
<variable name="g" units="first_order_rate_constant" public_interface="in"/>
<variable name="I_2" units="dimensionless" public_interface="in"/>
<variable name="P_1" units="dimensionless" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>R_2</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>alpha_2</ci>
<ci>I_2</ci>
</apply>
<apply>
<times/>
<ci>d</ci>
<ci>R_2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>g</ci>
<ci>R_2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>beta_1</ci>
<ci>R_2</ci>
<ci>P_1</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="R12">
<variable name="R_12" units="dimensionless" initial_value="0" public_interface="out"/>
<variable name="alpha_2" units="first_order_rate_constant" public_interface="in"/>
<variable name="alpha_1" units="first_order_rate_constant" public_interface="in"/>
<variable name="d" units="first_order_rate_constant" public_interface="in"/>
<variable name="g" units="first_order_rate_constant" public_interface="in"/>
<variable name="I_21" units="dimensionless" public_interface="in"/>
<variable name="I_12" units="dimensionless" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>R_12</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>alpha_2</ci>
<ci>I_12</ci>
</apply>
<apply>
<times/>
<ci>alpha_1</ci>
<ci>I_21</ci>
</apply>
</apply>
<apply>
<times/>
<ci>d</ci>
<ci>R_12</ci>
</apply>
</apply>
<apply>
<times/>
<ci>g</ci>
<ci>R_12</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="P1">
<variable name="P_1" units="dimensionless" initial_value="1" public_interface="out"/>
<variable name="k_1" units="first_order_rate_constant" initial_value="1"/>
<variable name="u" units="first_order_rate_constant" public_interface="in"/>
<variable name="I_1" units="dimensionless" public_interface="in"/>
<variable name="I_21" units="dimensionless" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<variable name="log_P1" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_1</ci>
<apply>
<plus/>
<ci>I_1</ci>
<ci>I_21</ci>
</apply>
</apply>
<apply>
<times/>
<ci>u</ci>
<ci>P_1</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>log_P1</ci>
<apply>
<log/>
<ci>P_1</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="P2">
<variable name="P_2" units="dimensionless" initial_value="1" public_interface="out"/>
<variable name="k_2" units="first_order_rate_constant" initial_value="1"/>
<variable name="u" units="first_order_rate_constant" public_interface="in"/>
<variable name="I_2" units="dimensionless" public_interface="in"/>
<variable name="I_12" units="dimensionless" public_interface="in"/>
<variable name="time" units="day" public_interface="in"/>
<variable name="log_P2" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>P_2</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_2</ci>
<apply>
<plus/>
<ci>I_2</ci>
<ci>I_12</ci>
</apply>
</apply>
<apply>
<times/>
<ci>u</ci>
<ci>P_2</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>log_P2</ci>
<apply>
<log/>
<ci>P_2</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="memory_duration">
<variable name="G" units="dimensionless"/>
<variable name="g" units="first_order_rate_constant" initial_value="0.01" public_interface="out"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>G</ci>
<apply>
<divide/>
<cn cellml:units="first_order_rate_constant">1</cn>
<ci>g</ci>
</apply>
</apply>
</math>
</component>
<component xmlns="http://www.cellml.org/cellml/1.0#" name="kinetic_parameters">
<variable name="beta_1" units="first_order_rate_constant" initial_value="1" public_interface="out"/>
<variable name="alpha_1" units="first_order_rate_constant" initial_value="0.1" public_interface="out"/>
<variable name="beta_2" units="first_order_rate_constant" initial_value="1" public_interface="out"/>
<variable name="alpha_2" units="first_order_rate_constant" initial_value="0.1" public_interface="out"/>
<variable name="a_1" units="first_order_rate_constant" initial_value="0.03" public_interface="out"/>
<variable name="a_2" units="first_order_rate_constant" initial_value="1" public_interface="out"/>
<variable name="d" units="first_order_rate_constant" initial_value="0.01" public_interface="out"/>
<variable name="u" units="first_order_rate_constant" initial_value="0.5" public_interface="out"/>
</component>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="S" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I12" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I21" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R12" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P1" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P2" component_2="environment"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="S" component_2="P1"/>
<map_variables variable_1="P_1" variable_2="P_1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="S" component_2="P2"/>
<map_variables variable_1="P_2" variable_2="P_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="S" component_2="R1"/>
<map_variables variable_1="R_1" variable_2="R_1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="S" component_2="R2"/>
<map_variables variable_1="R_2" variable_2="R_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="S" component_2="R12"/>
<map_variables variable_1="R_12" variable_2="R_12"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I1" component_2="S"/>
<map_variables variable_1="S" variable_2="S"/>
<map_variables variable_1="I_1" variable_2="I_1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I2" component_2="S"/>
<map_variables variable_1="S" variable_2="S"/>
<map_variables variable_1="I_2" variable_2="I_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I12" component_2="S"/>
<map_variables variable_1="I_12" variable_2="I_12"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I21" component_2="S"/>
<map_variables variable_1="I_21" variable_2="I_21"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I1" component_2="P1"/>
<map_variables variable_1="I_1" variable_2="I_1"/>
<map_variables variable_1="P_1" variable_2="P_1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I2" component_2="P2"/>
<map_variables variable_1="I_2" variable_2="I_2"/>
<map_variables variable_1="P_2" variable_2="P_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I21" component_2="P1"/>
<map_variables variable_1="I_21" variable_2="I_21"/>
<map_variables variable_1="P_1" variable_2="P_1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I12" component_2="P2"/>
<map_variables variable_1="I_12" variable_2="I_12"/>
<map_variables variable_1="P_2" variable_2="P_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R1" component_2="I1"/>
<map_variables variable_1="I_1" variable_2="I_1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R1" component_2="I12"/>
<map_variables variable_1="R_1" variable_2="R_1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R2" component_2="I21"/>
<map_variables variable_1="R_2" variable_2="R_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R2" component_2="I2"/>
<map_variables variable_1="I_2" variable_2="I_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R1" component_2="P2"/>
<map_variables variable_1="P_2" variable_2="P_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R2" component_2="P1"/>
<map_variables variable_1="P_1" variable_2="P_1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R12" component_2="I21"/>
<map_variables variable_1="I_21" variable_2="I_21"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R12" component_2="I12"/>
<map_variables variable_1="I_12" variable_2="I_12"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="S" component_2="kinetic_parameters"/>
<map_variables variable_1="d" variable_2="d"/>
<map_variables variable_1="beta_1" variable_2="beta_1"/>
<map_variables variable_1="beta_2" variable_2="beta_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I1" component_2="kinetic_parameters"/>
<map_variables variable_1="alpha_1" variable_2="alpha_1"/>
<map_variables variable_1="a_1" variable_2="a_1"/>
<map_variables variable_1="beta_1" variable_2="beta_1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I2" component_2="kinetic_parameters"/>
<map_variables variable_1="alpha_2" variable_2="alpha_2"/>
<map_variables variable_1="a_2" variable_2="a_2"/>
<map_variables variable_1="beta_2" variable_2="beta_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I21" component_2="kinetic_parameters"/>
<map_variables variable_1="alpha_1" variable_2="alpha_1"/>
<map_variables variable_1="a_1" variable_2="a_1"/>
<map_variables variable_1="beta_1" variable_2="beta_1"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="I12" component_2="kinetic_parameters"/>
<map_variables variable_1="alpha_2" variable_2="alpha_2"/>
<map_variables variable_1="a_2" variable_2="a_2"/>
<map_variables variable_1="beta_2" variable_2="beta_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R1" component_2="kinetic_parameters"/>
<map_variables variable_1="alpha_1" variable_2="alpha_1"/>
<map_variables variable_1="d" variable_2="d"/>
<map_variables variable_1="beta_2" variable_2="beta_2"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R2" component_2="kinetic_parameters"/>
<map_variables variable_1="alpha_2" variable_2="alpha_2"/>
<map_variables variable_1="beta_1" variable_2="beta_1"/>
<map_variables variable_1="d" variable_2="d"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R12" component_2="kinetic_parameters"/>
<map_variables variable_1="alpha_1" variable_2="alpha_1"/>
<map_variables variable_1="alpha_2" variable_2="alpha_2"/>
<map_variables variable_1="d" variable_2="d"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P1" component_2="kinetic_parameters"/>
<map_variables variable_1="u" variable_2="u"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="P2" component_2="kinetic_parameters"/>
<map_variables variable_1="u" variable_2="u"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="S" component_2="memory_duration"/>
<map_variables variable_1="g" variable_2="g"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R1" component_2="memory_duration"/>
<map_variables variable_1="g" variable_2="g"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R2" component_2="memory_duration"/>
<map_variables variable_1="g" variable_2="g"/>
</connection>
<connection xmlns="http://www.cellml.org/cellml/1.0#">
<map_components component_1="R12" component_2="memory_duration"/>
<map_variables variable_1="g" variable_2="g"/>
</connection>
</model>
