Location: Nelson, Murray, Perelson, 2000 @ 039700a89cc6 / nelson_murray_perelson_2000_general.cellml

Author:

Tessa Paris <tpar054@aucklanduni.ac.nz>

Date:

2010-02-19 14:53:24+13:00

Desc:

Split the model into the general and delay versions. Neither recreate the figure in the paper

Permanent Source URI:

http://models.cellml.org/workspace/nelson_murray_perelson_2000/rawfile/039700a89cc6491d6495f1f1fa790e5783838b3f/nelson_murray_perelson_2000_general.cellml

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This CellML file was generated on 20/01/2010 at 2:58:36 at p.m. using:

COR (0.9.31.1333)
Copyright 2002-2010 Dr Alan Garny
http://cor.physiol.ox.ac.uk/ - cor@physiol.ox.ac.uk

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http://www.cellml.org/
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				<title>A Model of HIV-1 Pathogenesis</title>
				<author>
					<firstname>Catherine</firstname>
					<surname>Lloyd</surname>
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						<shortaffil>Bioengineering Institute, University of Auckland</shortaffil>
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            This is the original unchecked version of the model imported from the previous
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				<title>Model Structure</title>
				<para>
In recent years, clinical research together with mathematical modelling has enhanced our understanding of HIV-1 infection dynamics.  For example, the introduction of a new class of antiretroviral drugs called protease inhibitors has helped to define the kinetic parameters underlying HIV-1 infection.  However, many of the mathematical models that have been developed have incorrectly assumed that drug treatments are 100 percent effective, and that upon infection, a cell immediately begins to produce virus. 
</para>
				<para>
In HIV-1 infection, the virus life cycle plays a crucial role in disease progression.  The binding of a viral particle to a receptor on a target T-cell initiates a cascade of of events that can lead to the targeted cell becoming productively infected, that is, producing new virus (see <xref linkend="fig_reaction_diagram"/> below).  There is a significant time delay between initial viral entry into a cell and subsequent viral production.    
</para>
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In 2000, Nelson <emphasis>et al.</emphasis> published a mathematical model of HIV-1 pathogenesis that included an intracellular delay in the initiation of virus production.  Their model also allowed for the fact that the effects of drugs can be less than perfect.  Analysis showed that when drug efficacy is less than perfect, as is frequently the case <emphasis>in vivo</emphasis>, the predicted rate of decline in plasma virus concentration depends on three factors: the death rate of infected, virus producing T-cells, the efficacy of the drug therapy, and the length of the time delay between infection of a T-cell and virus production.  From their model, Nelson <emphasis>et al.</emphasis> suggest that previous estimates of infected cell loss rates may be unrealistic and could be improved upon by considering more realistic models of viral infection.
</para>
				<para>
The complete original paper reference is cited below:
</para>
				<para>
A model of HIV-1 pathogenesis that includes an intracellular delay, Patrick W. Nelson, James D. Murray, and Alan S. Perelson, 2000, <emphasis>Mathematical Biosciences</emphasis>, 163, 201-215.  <ulink url="http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&amp;db=PubMed&amp;list_uids=10701304&amp;dopt=Abstract">PubMed ID: 10701304</ulink>
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								<title>reaction schematic for the model</title>
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					<caption>A schematic diagram showing the cascade of events triggered by the binding of a HIV-1 virus particle to a receptor on a target T-cell.</caption>
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         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="non_infectious_virus">
      <variable name="VNI" units="virons_per_ml" initial_value="0" public_interface="out"/>
      <variable name="delta" units="cells_per_day" public_interface="in"/>
      <variable name="time" units="day" public_interface="in"/>
      <variable name="N" units="virons_per_cell" public_interface="in"/>
      <variable name="np" units="dimensionless" public_interface="in"/>
      <variable name="c" units="virons_per_day" public_interface="in"/>
      <variable name="T_in" units="cells_per_mm3" public_interface="in"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <apply>
               <diff/>
               <bvar>
                  <ci>time</ci>
               </bvar>
               <ci>VNI</ci>
            </apply>
            <apply>
               <minus/>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>np</ci>
                     <ci>N</ci>
                     <ci>delta</ci>
                     <ci>T_in</ci>
                  </apply>
                  <apply>
                     <times/>
                     <cn cellml:units="cells_per_mm3">1</cn>
                     <cn cellml:units="ml">1</cn>
                  </apply>
               </apply>
               <apply>
                  <divide/>
                  <apply>
                     <times/>
                     <ci>c</ci>
                     <ci>VNI</ci>
                  </apply>
                  <cn cellml:units="viron">1</cn>
               </apply>
            </apply>
         </apply>
      </math>
   </component>
   <component xmlns="http://www.cellml.org/cellml/1.0#" name="total_virus">
      <variable name="VNI" units="virons_per_ml" public_interface="in"/>
      <variable name="VI" units="virons_per_ml" public_interface="in"/>
      <variable name="virus_total" units="virons_per_ml"/>
      <math xmlns="http://www.w3.org/1998/Math/MathML">
         <apply>
            <eq/>
            <ci>virus_total</ci>
            <apply>
               <plus/>
               <ci>VI</ci>
               <ci>VNI</ci>
            </apply>
         </apply>
      </math>
   </component>
   <group xmlns="http://www.cellml.org/cellml/1.0#">
      <relationship_ref relationship="containment"/>
      <component_ref component="environment">
         <component_ref component="uninfected_T_cells"/>
         <component_ref component="infected_T_cells"/>
         <component_ref component="infectious_virus"/>
         <component_ref component="non_infectious_virus"/>
         <component_ref component="total_virus"/>
      </component_ref>
   </group>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="uninfected_T_cells" component_2="environment"/>
      <map_variables variable_1="delta" variable_2="delta"/>
      <map_variables variable_1="delta_1" variable_2="delta_1"/>
      <map_variables variable_1="lambda" variable_2="lambda"/>
      <map_variables variable_1="k" variable_2="k"/>
      <map_variables variable_1="time" variable_2="time"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="infected_T_cells" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="k" variable_2="k"/>
      <map_variables variable_1="delta" variable_2="delta"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="infectious_virus" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="np" variable_2="np"/>
      <map_variables variable_1="N" variable_2="N"/>
      <map_variables variable_1="c" variable_2="c"/>
      <map_variables variable_1="delta" variable_2="delta"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="non_infectious_virus" component_2="environment"/>
      <map_variables variable_1="time" variable_2="time"/>
      <map_variables variable_1="np" variable_2="np"/>
      <map_variables variable_1="N" variable_2="N"/>
      <map_variables variable_1="c" variable_2="c"/>
      <map_variables variable_1="delta" variable_2="delta"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="uninfected_T_cells" component_2="infected_T_cells"/>
      <map_variables variable_1="T" variable_2="T"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="infected_T_cells" component_2="infectious_virus"/>
      <map_variables variable_1="T_in" variable_2="T_in"/>
      <map_variables variable_1="VI" variable_2="VI"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="infected_T_cells" component_2="non_infectious_virus"/>
      <map_variables variable_1="T_in" variable_2="T_in"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="uninfected_T_cells" component_2="infectious_virus"/>
      <map_variables variable_1="VI" variable_2="VI"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="total_virus" component_2="non_infectious_virus"/>
      <map_variables variable_1="VNI" variable_2="VNI"/>
   </connection>
   <connection xmlns="http://www.cellml.org/cellml/1.0#">
      <map_components component_1="total_virus" component_2="infectious_virus"/>
      <map_variables variable_1="VI" variable_2="VI"/>
   </connection>
</model>