- 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_delay.cellml
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<!--
This CellML file was generated on 12/02/2010 at 2:20:07 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
CellML 1.0 was used to generate this model
http://www.cellml.org/
-->
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<title>A Model of HIV-1 Pathogenesis</title>
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<title>Model Status</title>
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This the delay model from the paper. It runs in COR and OpenCell but it does not replicate the figures in the paper. The parameter 'm' is not known.
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ABSTRACT:
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Mathematical modeling combined with experimental measurements have yielded important insights into HIV-1 pathogenesis. For example, data from experiments in which HIV-infected patients are given potent antiretroviral drugs that perturb the infection process have been used to estimate kinetic parameters underlying HIV infection. Many of the models used to analyze data have assumed drug treatments to be completely efficacious and that upon infection a cell instantly begins producing virus. We consider a model that allows for less then perfect drug effects and which includes a delay in the initiation of virus production. We present detailed analysis of this delay differential equation model and compare the results to a model without delay. Our analysis shows that when drug efficacy is less than 100%, as may be the case in vivo, the predicted rate of decline in plasma virus concentration depends on three factors: the death rate of virus producing cells, the efficacy of therapy, and the length of the delay. Thus, previous estimates of infected cell loss rates can be improved upon by considering more realistic models of viral infection..
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The complete original paper reference is cited below:
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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/pubmed/10701304?dopt=Abstract">PubMed ID: 10701304</ulink>
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A model of HIV-1 pathogenesis that includes an intracellular delay
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</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"/>
<map_variables variable_1="tau" variable_2="tau"/>
<map_variables variable_1="m" variable_2="m"/>
</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="T0" variable_2="T0"/>
</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>
