- Author:
- Tessa Paris <tpar054@aucklanduni.ac.nz>
- Date:
- 2010-01-13 11:23:19+13:00
- Desc:
- Removed dead links and changed the model status
- Permanent Source URI:
- https://models.cellml.org/workspace/wodarz_2003/rawfile/efc89258315aaee61900622e93734f245e69e55f/wodarz_2003.cellml
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<title>Modelling the Evolution of Immunological Memory</title>
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<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
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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.
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<title>Model Structure</title>
<para>
Memory is an important characteristic of immune responses. Immunological memory is defined as an increased number of specific immune cells that remain in the body after an infection has been resolved, and they function to protect the host against reinfection. The exact process by which immunological memory evolves is not fully known. To date, suggestions for the advantages which might drive the evolution of memory include: protection from reinfection, control of long-term infections, and the transfer of immune function to the next generation.
</para>
<para>
In this study by Wodarz, two mathematical models are developed to investigate new potential advantages that could drive the evolution of immunological memory (see figure 1 and figure 2 below). Although mathematical analysis clearly shows that a longer duration of memory is advantageous for the host in that it protects against reinfection, it may also allow another, inferior pathogen species to persist. This can be a significant disadvantage to the host if the inferior pathogen is more virulent. In the absence of pathogen diversity, memory is expected to evolve to a long duration, but with increased pathogen diversity and under certain specific conditions, memory can evolve towards shorter durations.
</para>
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The complete 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>
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<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>
