Rendering of the source text

<?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 -->
	<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:title>Modeling defective interfering virus therapy for AIDS: conditions for DIV survival (DIV Interference)</dc:title>
			<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>2010-01-26</dcterms:W3CDTF>
			</dcterms:created>
		</rdf:Description>
		<rdf:Description rdf:about="#nelson_1995b">
			<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Modeling defective interfering virus therapy for AIDS: conditions for DIV survival</dc:title>
			<cmeta:comment rdf:parseType="Resource">
				<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>
				<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>Keywords</bqs:subject_type>
					<rdf:value>
						<rdf:Bag>
							<rdf:li>Immunology</rdf:li>
							<rdf:li>CD4 T cell</rdf:li>
							<rdf:li>HIV-1</rdf:li>
							<rdf:li>dynamics</rdf:li>
							<rdf:li>DIV</rdf:li>
							<rdf:li>engineered virus</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>7881191</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>Nelson</vCard:Family>
										<vCard:Given>George</vCard:Given>
										<vCard:Other>W</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>Perelson</vCard:Family>
										<vCard:Given>Alan</vCard:Given>
										<vCard:Other>S</vCard:Other>
									</vCard:N>
								</bqs:Person>
							</rdf:li>
						</rdf:Seq>
					</dc:creator>
					<dc:title xmlns:dc="http://purl.org/dc/elements/1.1/">Modeling defective interfering virus therapy for AIDS: conditions for DIV survival</dc:title>
					<dcterms:issued xmlns:dcterms="http://purl.org/dc/terms/" rdf:parseType="Resource">
						<dcterms:W3CDTF>1995-02</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>125</bqs:volume>
					<bqs:first_page>127</bqs:first_page>
					<bqs:last_page>153</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>