<?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 defective interfering virus therapy for AIDS: conditions for DIV survival</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 (equations 1-3, and 7-13). This file is known to run in OpenCell and COR, and uses the parameters values in Tables 1, 2, and 3 of the paper. One of the units (for the variable theta) has been changed from micro_L (in the paper), to per_micro_L, to be dimensionally consistent. Parameters in years are represented in day equivalents. 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="nelson_1995.png"/>
</imageobject>
</mediaobject>
<caption>Schematic illustration of the main features of the model.</caption>
</informalfigure>
<para>The original paper reference is cited below:</para>
<para>Modeling defective interfering virus therapy for AIDS: conditions for DIV survival, Nelson G, Perelson A, 1995, <emphasis>Mathematical Biosciences</emphasis>, 125, 127-153. <ulink url="http://www.ncbi.nlm.nih.gov/pubmed/7881191">PubMed ID: 7881191</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 -->
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<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"/>
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<apply>
<diff/>
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<ci>time</ci>
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<ci>T</ci>
</apply>
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<minus/>
<apply>
<minus/>
<apply>
<plus/>
<apply>
<minus/>
<ci>s_V</ci>
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<times/>
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<times/>
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<minus/>
<cn xmlns:cellml="http://www.cellml.org/cellml/1.0#" cellml:units="dimensionless">1</cn>
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<divide/>
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<ci>T_1</ci>
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</apply>
</apply>
</apply>
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<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>
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<eq/>
<ci>s_V</ci>
<apply>
<divide/>
<apply>
<times/>
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<ci>theta</ci>
</apply>
<apply>
<plus/>
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</apply>
</apply>
</apply>
</math>
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<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"/>
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<apply>
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<apply>
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<times/>
<ci>k_1_</ci>
<ci>V_</ci>
<ci>T</ci>
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<times/>
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<ci>T_1</ci>
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<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"/>
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<minus/>
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<minus/>
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<ci>k_2</ci>
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<times/>
<ci>k_1D</ci>
<ci>D</ci>
<ci>T_2</ci>
</apply>
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<apply>
<times/>
<ci>mu_b</ci>
<ci>T_2</ci>
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</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/>
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<ci>time</ci>
</bvar>
<ci>T_D2</ci>
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<apply>
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<times/>
<ci>mu_bD</ci>
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</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"/>
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<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/>
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<ci>t_DIV</ci>
</apply>
<apply>
<lt/>
<ci>time</ci>
<ci>t_DIV</ci>
</apply>
</piece>
<otherwise>
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<apply>
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<times/>
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<times/>
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<ci>D_ode</ci>
</apply>
</apply>
</otherwise>
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<times/>
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<ci>N_t</ci>
</apply>
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<eq/>
<ci>pi_D_t</ci>
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<times/>
<cn cellml:units="dimensionless">0.5</cn>
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<ci>N_t</ci>
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<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"/>
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<eq/>
<apply>
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</bvar>
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<minus/>
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<plus/>
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<times/>
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<ci>mu_b</ci>
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<eq/>
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<times/>
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<ci>N_t</ci>
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</apply>
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<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"/>
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<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">
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<power/>
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<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/>
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<ci>T_1</ci>
<ci>T_2</ci>
<ci>T_D2</ci>
<ci>T_D1</ci>
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</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>
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</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 -->
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<dc:title>Modeling defective interfering virus therapy for AIDS: conditions for DIV survival (DIV Interference)</dc:title>
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<rdf:value>This is the CellML description of Nelson and Perelson's 1995 mathematical model for a defective interfering virus therapy for AIDS</rdf:value>
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<!-- Keywords -->
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<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Mathematical Biosciences</dc:title>
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<!-- OpenCell metadata -->
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<simulation xmlns="http://www.cellml.org/metadata/simulation/1.0#">
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<connection>
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<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>
