- Author:
- Ethan Choi <mcho099@aucklanduni.ac.nz>
- Date:
- 2010-02-19 16:07:06+13:00
- Desc:
- Created model b. Runs in OpenCell and COR however does not replicate figures.
Needs curating.
- Permanent Source URI:
- https://models.cellml.org/workspace/nelson_perelson_1995/rawfile/696a51e90adb9c230bfe844ceb51e40edfd46460/nelson_1995b.cellml
<?xml version="1.0"?>
<!-- FILE : nelson_1995b.cellml
CREATED : 20th Jan 2010
LAST MODIFIED : 25th Jan 2010
AUTHOR : Ethan Choi
MODEL STATUS : This model conforms to the CellML 1.1 Specification. Runs in OpenCell
DESCRIPTION : This file contains a CellML description of Nelson's 1993 mathematical model for a defective interfering virus-->
<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="nelson_1995b" cmeta:id="nelson_1995b" 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 -->
<documentation xmlns="http://cellml.org/tmp-documentation">
<article>
<articleinfo>
<title>Modeling </title>
<author>
<firstname>Ethan</firstname>
<surname>Choi</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 has been built with the differential expressions in Nelson and Perelson's 1995 paper for the model with DIV interference (nelson_1995b). This file is known to run in OpenCell and COR, and is set to the parameters in Table 1, 2, and 3 of the paper. One the unit (theta) has been changed from micro_L (in the paper), to per_micro_L, to be dimensionally homogeneous. Parameters in years are represented in day equivalents. The model does not recreate the figures and need to be curated (something wrong with the DIV). In order to model the inoculum of DIV (an ODE that must have an initial condition at a certain time), a function was created to get the value up to the initial condition, then swapped out via a piecewise.</para>
</section>
<sect1 id="sec_structure">
<title>Model Structure</title>
<para>ABSTRACT: The administration of a genetically engineered defective interfering virus (DIV) that interferes with HIV-1 replication has been proposed as a therapy for HIV-1 infection and AIDS. The proposed interfering virus, which is designed to superinfect HIV-1 infected cells, carries ribozymes that cleave conserved regions in HIV-1 RNA that code for the viral envelope protein. Thus DIV infection of HIV-1 infected cells should reduce or eliminate viral production by these cells. The success of this therapeutic strategy will depend both on the intercellular interaction of DIV and HIV-1, and on the overall dynamics of virus and T cells in the body. To study these dynamical issues, we have constructed a mathematical model of the interaction of HIV-1, DIV, and CD4+ cells in vivo. The results of both mathematical analysis and numerical simulation indicate that survival of the engineered DIV purely on a peripheral blood HIV-1 infection is unlikely. However, analytical results indicate that DIV might well survive on HIV-1 infected CD4+ cells in lymphoid organs such as lymph nodes and spleen, or on other HIV-1 infected cells in these organs.</para>
<informalfigure float="0" id="fig_reaction_diagram">
<mediaobject>
<imageobject>
<objectinfo>
<title>model diagram</title>
</objectinfo>
<imagedata fileref="perelson_1993.png"/>
</imageobject>
</mediaobject>
<caption>Schematic diagram of the model.</caption>
</informalfigure>
<para>The original paper reference is cited below:</para>
<para>
Dynamics of HIV infection of CD4+ T cells, Perelson, Kirschner, Boer, <emphasis>Mathematical Biosciences</emphasis>
, 114, 81-125. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/8096155">PubMed ID: 8096155</ulink>
</para>
</sect1>
</article>
</documentation>
<!-- units -->
<units name="day">
<unit multiplier="86400" units="second"/>
</units>
<units name="per_day">
<unit exponent="-1" units="day"/>
</units>
<units name="year">
<unit multiplier="365.24" units="day"/>
</units>
<units name="micro_L">
<unit prefix="micro" units="litre"/>
</units>
<units name="per_micro_L">
<unit exponent="-1" units="micro_L"/>
</units>
<units name="micro_L_per_day">
<unit units="micro_L"/>
<unit units="per_day"/>
</units>
<units name="per_micro_L_day">
<unit units="per_micro_L"/>
<unit units="per_day"/>
</units>
<!-- components -->
<component name="environment">
<variable name="time" public_interface="out" units="day"/>
</component>
<component name="uninfected_CD4">
<variable name="time" public_interface="in" units="day"/>
<variable initial_value="0.02" name="mu_T" public_interface="out" units="per_day"/>
<variable initial_value="0.03" name="r" units="per_day"/>
<variable name="T_1" public_interface="in" units="per_micro_L"/>
<variable initial_value="1500" name="T_max" units="per_micro_L"/>
<variable name="k_1" public_interface="in" units="micro_L_per_day"/>
<variable name="V" public_interface="in" units="per_micro_L"/>
<variable name="k_1_" public_interface="in" units="micro_L_per_day"/>
<variable name="V_" public_interface="in" units="per_micro_L"/>
<variable initial_value="10" name="s_0" units="per_micro_L_day"/>
<variable initial_value="1" name="theta" units="per_micro_L"/>
<variable name="s_V" units="per_micro_L_day"/>
<variable initial_value="1000" name="T" public_interface="out" units="per_micro_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>T</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>s_V</ci>
<apply>
<times/>
<ci>mu_T</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<times/>
<ci>r</ci>
<ci>T</ci>
<apply>
<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
<apply>
<divide/>
<apply>
<plus/>
<ci>T</ci>
<ci>T_1</ci>
</apply>
<ci>T_max</ci>
</apply>
</apply>
</apply>
</apply>
<apply>
<times/>
<ci>k_1</ci>
<ci>V</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_1_</ci>
<ci>V_</ci>
<ci>T</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>s_V</ci>
<apply>
<divide/>
<apply>
<times/>
<ci>s_0</ci>
<ci>theta</ci>
</apply>
<apply>
<plus/>
<ci>theta</ci>
<ci>V</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="latently_infected_CD4">
<variable name="time" public_interface="in" units="day"/>
<variable name="k_1" public_interface="in" units="micro_L_per_day"/>
<variable name="V" public_interface="in" units="per_micro_L"/>
<variable name="T" public_interface="in" units="per_micro_L"/>
<variable name="k_1_" public_interface="in" units="micro_L_per_day"/>
<variable name="V_" public_interface="in" units="per_micro_L"/>
<variable name="mu_T" public_interface="in" units="per_day"/>
<variable initial_value="0.017" name="k_2" public_interface="out" units="per_day"/>
<variable initial_value="0" name="T_1" public_interface="out" units="per_micro_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>T_1</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>k_1</ci>
<ci>V</ci>
<ci>T</ci>
</apply>
<apply>
<times/>
<ci>k_1_</ci>
<ci>V_</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<times/>
<ci>mu_T</ci>
<ci>T_1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_2</ci>
<ci>T_1</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="actively_infected_CD4">
<variable name="time" public_interface="in" units="day"/>
<variable name="k_2" public_interface="in" units="per_day"/>
<variable name="T_1" public_interface="in" units="per_micro_L"/>
<variable initial_value="2.4E-5" name="k_1D" public_interface="out" units="micro_L_per_day"/>
<variable name="D" public_interface="in" units="per_micro_L"/>
<variable initial_value="0.24" name="mu_b" public_interface="out" units="per_day"/>
<variable initial_value="0" name="T_2" public_interface="out" units="per_micro_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>T_2</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>k_2</ci>
<ci>T_1</ci>
</apply>
<apply>
<times/>
<ci>k_1D</ci>
<ci>D</ci>
<ci>T_2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>mu_b</ci>
<ci>T_2</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="actively_coinfected_CD4">
<variable name="time" public_interface="in" units="day"/>
<variable name="k_1D" public_interface="in" units="micro_L_per_day"/>
<variable name="D" public_interface="in" units="per_micro_L"/>
<variable name="T_2" public_interface="in" units="per_micro_L"/>
<variable initial_value="0.48" name="k_s" public_interface="out" units="per_day"/>
<variable initial_value="0.12" name="mu_bD" public_interface="out" units="per_day"/>
<variable initial_value="0" name="T_D2" public_interface="out" units="per_micro_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>T_D2</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<times/>
<ci>k_1D</ci>
<ci>D</ci>
<ci>T_2</ci>
</apply>
<apply>
<times/>
<ci>k_s</ci>
<ci>T_D2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>mu_bD</ci>
<ci>T_D2</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="stably_coinfected_CD4">
<variable name="time" public_interface="in" units="day"/>
<variable name="k_s" public_interface="in" units="per_day"/>
<variable name="T_D2" public_interface="in" units="per_micro_L"/>
<variable initial_value="0.02" name="mu_TD" units="per_day"/>
<variable initial_value="0" name="T_D1" public_interface="out" units="per_micro_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>T_D1</ci>
</apply>
<apply>
<minus/>
<apply>
<times/>
<ci>k_s</ci>
<ci>T_D2</ci>
</apply>
<apply>
<times/>
<ci>mu_TD</ci>
<ci>T_D1</ci>
</apply>
</apply>
</apply>
</math>
</component>
<component name="DIV">
<variable name="time" public_interface="in" units="day"/>
<variable name="N_D_t" units="dimensionless"/>
<variable name="mu_bD" public_interface="in" units="per_day"/>
<variable name="T_D2" public_interface="in" units="per_micro_L"/>
<variable name="pi_D_t" units="per_day"/>
<variable name="T_D1" public_interface="in" units="per_micro_L"/>
<variable initial_value="0.76" name="mu_D" units="per_day"/>
<variable name="D" public_interface="out" units="per_micro_L"/>
<variable name="N_t" public_interface="in" units="dimensionless"/>
<variable name="mu_b" public_interface="in" units="per_day"/>
<variable initial_value="2557" name="t_DIV" units="day"/>
<variable initial_value="0" name="D_ode" units="per_micro_L"/>
<variable initial_value="0.1" name="D_0" units="per_micro_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>D</ci>
<piecewise>
<piece>
<cn cellml:units="per_micro_L">0</cn>
<apply>
<lt/>
<ci>time</ci>
<ci>t_DIV</ci>
</apply>
</piece>
<otherwise>
<ci>D_ode</ci>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>D_ode</ci>
</apply>
<piecewise>
<piece>
<apply>
<divide/>
<ci>D_0</ci>
<ci>t_DIV</ci>
</apply>
<apply>
<lt/>
<ci>time</ci>
<ci>t_DIV</ci>
</apply>
</piece>
<otherwise>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>N_D_t</ci>
<ci>mu_bD</ci>
<ci>T_D2</ci>
</apply>
<apply>
<times/>
<ci>pi_D_t</ci>
<ci>T_D1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>mu_D</ci>
<ci>D_ode</ci>
</apply>
</apply>
</otherwise>
</piecewise>
</apply>
<apply>
<eq/>
<ci>N_D_t</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.2</cn>
<ci>N_t</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>pi_D_t</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.5</cn>
<ci>mu_b</ci>
<ci>N_t</ci>
</apply>
</apply>
</math>
</component>
<component name="HIV1">
<variable name="time" public_interface="in" units="day"/>
<variable name="N_t" public_interface="in" units="dimensionless"/>
<variable name="mu_b" public_interface="in" units="per_day"/>
<variable name="T_2" public_interface="in" units="per_micro_L"/>
<variable name="N_2_t" units="dimensionless"/>
<variable name="mu_bD" public_interface="in" units="per_day"/>
<variable name="T_D2" public_interface="in" units="per_micro_L"/>
<variable initial_value="2.4E-5" name="k_1" public_interface="out" units="micro_L_per_day"/>
<variable name="T" public_interface="in" units="per_micro_L"/>
<variable initial_value="2.4" name="mu_V" public_interface="out" units="per_day"/>
<variable initial_value="1E-3" name="V" public_interface="out" units="per_micro_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>N_t</ci>
<ci>mu_b</ci>
<ci>T_2</ci>
</apply>
<apply>
<times/>
<ci>N_2_t</ci>
<ci>mu_bD</ci>
<ci>T_D2</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_1</ci>
<ci>V</ci>
<ci>T</ci>
</apply>
</apply>
<apply>
<times/>
<ci>mu_V</ci>
<ci>V</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>N_2_t</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.1</cn>
<ci>N_t</ci>
</apply>
</apply>
</math>
</component>
<component name="hybrid_HIV1">
<variable name="time" public_interface="in" units="day"/>
<variable name="N_t_" units="dimensionless"/>
<variable name="mu_bD" public_interface="in" units="per_day"/>
<variable name="T_D2" public_interface="in" units="per_micro_L"/>
<variable name="pi_t_" units="per_day"/>
<variable name="T_D1" public_interface="in" units="per_micro_L"/>
<variable name="mu_V" public_interface="in" units="per_day"/>
<variable initial_value="2.4E-7" name="k_1_" public_interface="out" units="micro_L_per_day"/>
<variable name="T" public_interface="in" units="per_micro_L"/>
<variable initial_value="0" name="V_" public_interface="out" units="per_micro_L"/>
<variable name="mu_b" public_interface="in" units="per_day"/>
<variable name="N_t" public_interface="in" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<apply>
<diff/>
<bvar>
<ci>time</ci>
</bvar>
<ci>V_</ci>
</apply>
<apply>
<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<times/>
<ci>N_t_</ci>
<ci>mu_bD</ci>
<ci>T_D2</ci>
</apply>
<apply>
<times/>
<ci>pi_t_</ci>
<ci>T_D1</ci>
</apply>
</apply>
<apply>
<times/>
<ci>mu_V</ci>
<ci>V_</ci>
</apply>
</apply>
<apply>
<times/>
<ci>k_1_</ci>
<ci>T</ci>
<ci>V_</ci>
</apply>
</apply>
</apply>
<apply>
<eq/>
<ci>N_t_</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.1</cn>
<ci>N_t</ci>
</apply>
</apply>
<apply>
<eq/>
<ci>pi_t_</ci>
<apply>
<times/>
<cn cellml:units="dimensionless">0.01</cn>
<ci>mu_b</ci>
<ci>N_t</ci>
</apply>
</apply>
</math>
</component>
<component name="production_function">
<variable name="time" public_interface="in" units="day"/>
<variable initial_value="300" name="N_0" units="dimensionless"/>
<variable initial_value="25" name="gamma" units="dimensionless"/>
<variable initial_value="7305" name="t_c" units="day"/>
<variable name="N_t" public_interface="out" units="dimensionless"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>N_t</ci>
<apply>
<times/>
<ci>N_0</ci>
<apply>
<plus/>
<cn cellml:units="dimensionless">1</cn>
<apply>
<times/>
<ci>gamma</ci>
<apply>
<divide/>
<apply>
<power/>
<ci>time</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<plus/>
<apply>
<power/>
<ci>time</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
<apply>
<power/>
<ci>t_c</ci>
<cn cellml:units="dimensionless">2</cn>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</apply>
</math>
</component>
<component name="cell_population">
<variable name="T" public_interface="in" units="per_micro_L"/>
<variable name="T_1" public_interface="in" units="per_micro_L"/>
<variable name="T_2" public_interface="in" units="per_micro_L"/>
<variable name="T_D2" public_interface="in" units="per_micro_L"/>
<variable name="T_D1" public_interface="in" units="per_micro_L"/>
<variable name="T_tot" units="per_micro_L"/>
<math xmlns="http://www.w3.org/1998/Math/MathML">
<apply>
<eq/>
<ci>T_tot</ci>
<apply>
<plus/>
<ci>T</ci>
<ci>T_1</ci>
<ci>T_2</ci>
<ci>T_D2</ci>
<ci>T_D1</ci>
</apply>
</apply>
</math>
</component>
<!-- connections -->
<connection>
<map_components component_1="environment" component_2="uninfected_CD4"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="latently_infected_CD4"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="actively_infected_CD4"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="actively_coinfected_CD4"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="stably_coinfected_CD4"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="DIV"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="HIV1"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="hybrid_HIV1"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="environment" component_2="production_function"/>
<map_variables variable_1="time" variable_2="time"/>
</connection>
<connection>
<map_components component_1="uninfected_CD4" component_2="latently_infected_CD4"/>
<map_variables variable_1="mu_T" variable_2="mu_T"/>
<map_variables variable_1="T_1" variable_2="T_1"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
<connection>
<map_components component_1="latently_infected_CD4" component_2="HIV1"/>
<map_variables variable_1="k_1" variable_2="k_1"/>
<map_variables variable_1="V" variable_2="V"/>
</connection>
<connection>
<map_components component_1="uninfected_CD4" component_2="HIV1"/>
<map_variables variable_1="k_1" variable_2="k_1"/>
<map_variables variable_1="V" variable_2="V"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
<connection>
<map_components component_1="uninfected_CD4" component_2="hybrid_HIV1"/>
<map_variables variable_1="k_1_" variable_2="k_1_"/>
<map_variables variable_1="V_" variable_2="V_"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
<connection>
<map_components component_1="latently_infected_CD4" component_2="hybrid_HIV1"/>
<map_variables variable_1="k_1_" variable_2="k_1_"/>
<map_variables variable_1="V_" variable_2="V_"/>
</connection>
<connection>
<map_components component_1="latently_infected_CD4" component_2="actively_infected_CD4"/>
<map_variables variable_1="T_1" variable_2="T_1"/>
<map_variables variable_1="k_2" variable_2="k_2"/>
</connection>
<connection>
<map_components component_1="actively_infected_CD4" component_2="actively_coinfected_CD4"/>
<map_variables variable_1="k_1D" variable_2="k_1D"/>
<map_variables variable_1="T_2" variable_2="T_2"/>
</connection>
<connection>
<map_components component_1="actively_infected_CD4" component_2="DIV"/>
<map_variables variable_1="D" variable_2="D"/>
<map_variables variable_1="mu_b" variable_2="mu_b"/>
</connection>
<connection>
<map_components component_1="actively_coinfected_CD4" component_2="DIV"/>
<map_variables variable_1="D" variable_2="D"/>
<map_variables variable_1="mu_bD" variable_2="mu_bD"/>
<map_variables variable_1="T_D2" variable_2="T_D2"/>
</connection>
<connection>
<map_components component_1="actively_infected_CD4" component_2="HIV1"/>
<map_variables variable_1="mu_b" variable_2="mu_b"/>
<map_variables variable_1="T_2" variable_2="T_2"/>
</connection>
<connection>
<map_components component_1="actively_coinfected_CD4" component_2="stably_coinfected_CD4"/>
<map_variables variable_1="k_s" variable_2="k_s"/>
<map_variables variable_1="T_D2" variable_2="T_D2"/>
</connection>
<connection>
<map_components component_1="actively_coinfected_CD4" component_2="HIV1"/>
<map_variables variable_1="mu_bD" variable_2="mu_bD"/>
<map_variables variable_1="T_D2" variable_2="T_D2"/>
</connection>
<connection>
<map_components component_1="actively_coinfected_CD4" component_2="hybrid_HIV1"/>
<map_variables variable_1="mu_bD" variable_2="mu_bD"/>
<map_variables variable_1="T_D2" variable_2="T_D2"/>
</connection>
<connection>
<map_components component_1="actively_infected_CD4" component_2="hybrid_HIV1"/>
<map_variables variable_1="mu_b" variable_2="mu_b"/>
</connection>
<connection>
<map_components component_1="stably_coinfected_CD4" component_2="DIV"/>
<map_variables variable_1="T_D1" variable_2="T_D1"/>
</connection>
<connection>
<map_components component_1="DIV" component_2="production_function"/>
<map_variables variable_1="N_t" variable_2="N_t"/>
</connection>
<connection>
<map_components component_1="HIV1" component_2="production_function"/>
<map_variables variable_1="N_t" variable_2="N_t"/>
</connection>
<connection>
<map_components component_1="hybrid_HIV1" component_2="production_function"/>
<map_variables variable_1="N_t" variable_2="N_t"/>
</connection>
<connection>
<map_components component_1="HIV1" component_2="hybrid_HIV1"/>
<map_variables variable_1="mu_V" variable_2="mu_V"/>
</connection>
<connection>
<map_components component_1="stably_coinfected_CD4" component_2="hybrid_HIV1"/>
<map_variables variable_1="T_D1" variable_2="T_D1"/>
</connection>
<connection>
<map_components component_1="cell_population" component_2="uninfected_CD4"/>
<map_variables variable_1="T" variable_2="T"/>
</connection>
<connection>
<map_components component_1="cell_population" component_2="latently_infected_CD4"/>
<map_variables variable_1="T_1" variable_2="T_1"/>
</connection>
<connection>
<map_components component_1="cell_population" component_2="actively_infected_CD4"/>
<map_variables variable_1="T_2" variable_2="T_2"/>
</connection>
<!-- metadata -->
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:about="">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Family>Choi</vCard:Family>
<vCard:Given>Ethan</vCard:Given>
</vCard:N>
<vCard:EMAIL xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<rdf:value>mcho099@aucklanduni.ac.nz</rdf:value>
<rdf:type rdf:resource="http://imc.org/vCard/3.0#internet"/>
</vCard:EMAIL>
<vCard:ORG xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Orgname>The University of Auckland</vCard:Orgname>
<vCard:Orgunit>Auckland Bioengineering Institute</vCard:Orgunit>
</vCard:ORG>
</dc:creator>
<dcterms:created xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource">
<dcterms:W3CDTF>2010-01-13</dcterms:W3CDTF>
</dcterms:created>
</rdf:Description>
<rdf:Description rdf:about="#nelson_1995b">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Dynamics of HIV infection of CD4+ T cells</dc:title>
<cmeta:comment rdf:parseType="Resource">
<rdf:value>This is the CellML description of Perelson, Kirschner, and Boer's 1993 mathematical model for the dynamics of HIV infection of CD4+ T cells</rdf:value>
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource">
<vCard:FN xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#">Ethan Choi</vCard:FN>
</dc:creator>
</cmeta:comment>
<cmeta:bio_entity>CD4+ T cell</cmeta:bio_entity>
<!-- Keywords -->
<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource">
<dc:subject xmlns:dc="http://purl.org/dc/elements/1.1/" rdf:parseType="Resource">
<bqs:subject_type>keyword</bqs:subject_type>
<rdf:value>
<rdf:Bag>
<rdf:li>Immunology</rdf:li>
<rdf:li>CD4 T cell</rdf:li>
<rdf:li>HIV</rdf:li>
<rdf:li>dynamics</rdf:li>
<rdf:li>AZT</rdf:li>
</rdf:Bag>
</rdf:value>
</dc:subject>
</bqs:reference>
<bqs:reference xmlns:bqs="http://www.cellml.org/bqs/1.0#" rdf:parseType="Resource">
<bqs:Pubmed_id>8096155</bqs:Pubmed_id>
<bqs:JournalArticle rdf:parseType="Resource">
<dc:creator xmlns:dc="http://purl.org/dc/elements/1.1/">
<rdf:Seq>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Family>Perelson</vCard:Family>
<vCard:Given>Alan</vCard:Given>
<vCard:Other>S</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Family>Kirschner</vCard:Family>
<vCard:Given>Denise</vCard:Given>
<vCard:Other>E</vCard:Other>
</vCard:N>
</bqs:Person>
</rdf:li>
<rdf:li rdf:parseType="Resource">
<bqs:Person rdf:parseType="Resource">
<vCard:N xmlns:vCard="http://www.w3.org/2001/vcard-rdf/3.0#" rdf:parseType="Resource">
<vCard:Family>de Boer</vCard:Family>
<vCard:Given>Rob</vCard:Given>
</vCard:N>
</bqs:Person>
</rdf:li>
</rdf:Seq>
</dc:creator>
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Dynamics of HIV infection of CD4+ T cells</dc:title>
<dcterms:issued xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource">
<dcterms:W3CDTF>1993-03</dcterms:W3CDTF>
</dcterms:issued>
<bqs:Journal rdf:parseType="Resource">
<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Mathematical Biosciences</dc:title>
</bqs:Journal>
<bqs:volume>114</bqs:volume>
<bqs:first_page>81</bqs:first_page>
<bqs:last_page>125</bqs:last_page>
</bqs:JournalArticle>
</bqs:reference>
</rdf:Description>
</rdf:RDF>
<!-- OpenCell metadata -->
<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#">
<rdf:Description rdf:nodeID="n1">
<boundIntervals xmlns="http://www.cellml.org/metadata/simulation/1.0#">
<rdf:Description rdf:nodeID="n2"/>
</boundIntervals>
</rdf:Description>
<rdf:Description rdf:nodeID="n2">
<rdf:first>
<rdf:Description rdf:nodeID="n3"/>
</rdf:first>
<rdf:rest>
<rdf:Description rdf:about="http://www.w3.org/1999/02/22-rdf-syntax-ns#nil"/>
</rdf:rest>
</rdf:Description>
<rdf:Description rdf:nodeID="n3">
<endingValue xmlns="http://www.cellml.org/metadata/simulation/1.0#" xml:lang="en">4383</endingValue>
<pointDensity xmlns="http://www.cellml.org/metadata/simulation/1.0#nonstandard-" xml:lang="en">100000</pointDensity>
</rdf:Description>
<rdf:Description rdf:about="#nelson_1995b">
<simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#">
<rdf:Description rdf:nodeID="n1"/>
</simulation>
</rdf:Description>
</rdf:RDF>
<connection>
<map_components component_1="cell_population" component_2="actively_coinfected_CD4"/>
<map_variables variable_1="T_D2" variable_2="T_D2"/>
</connection>
<connection>
<map_components component_1="cell_population" component_2="stably_coinfected_CD4"/>
<map_variables variable_1="T_D1" variable_2="T_D1"/>
</connection>
</model>
