A model of HIV-1 pathogenesis that includes an intracellular delay
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model represents the delay model from the paper, based on equation 4. The CellML model runs in both COR and OpenCell and the units are consistent. The model simulation output looks reasonable - with the exception of infectious T cells and noninfectious virus which have negative values in the early stages of the simulation. This should be physiologically impossible. The parameter value of the variable 'm' is unknown.
Model Structure
ABSTRACT: 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..
The original paper reference is cited below:
A model of HIV-1 pathogenesis that includes an intracellular delay, Patrick W. Nelson, James D. Murray, and Alan S. Perelson, 2000, Mathematical Biosciences, 163, 201-215. PubMed ID: 10701304
reaction schematic for the model
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.
viral dynamics
hiv-1
immunology
A model of HIV-1 pathogenesis that includes an intracellular delay (Delay Model)
The University of Auckland, Auckland Bioengineering Institute
This is the CellML description of Nelson et al's 2000 mathematical
model of HIV-1 pathogenesis.
Autumn
Cuellar
A
Peter
Villiger
J
2000-02
Catherine
Lloyd
May
keyword
James
Murray
D
10701304
Added publication date information.
Patrick
Nelson
W
The University of Auckland
Auckland Bioengineering Institute
2003-04-09
c.lloyd@auckland.ac.nz
Nelson et al's 2000 mathematical model of HIV-1 pathogenesis.
T-cells
A model of HIV-1 pathogenesis that includes an intracellular delay
163
201
215
2002-12-05
Corrected syntax error with base_units
Mathematical Biosciences
Catherine Lloyd
Alan
Perelson
S
2005-04-20
$T=180.0$
$\frac{d \mathrm{T\_star}}{d \mathrm{time}}=kT\mathrm{VI}(\mathrm{time}-\mathrm{tau})e^{-m\mathrm{tau}}\times 1-\frac{\mathrm{delta}}{1}\mathrm{T\_star}$
$\frac{d \mathrm{VI}}{d \mathrm{time}}=\frac{(1-\mathrm{np})N\mathrm{delta}\mathrm{T\_star}}{1}-\frac{c\mathrm{VI}}{1}\mathrm{log\_VI}=\lg \left(\frac{\mathrm{VI}}{1}\right)$
$\frac{d \mathrm{VNI}}{d \mathrm{time}}=\frac{\mathrm{np}N\mathrm{delta}\mathrm{T\_star}}{1}-\frac{c\mathrm{VNI}}{1}$
$\mathrm{virus\_total}=\mathrm{VI}+\mathrm{VNI}\mathrm{log\_virus\_total}=\lg \left(\frac{\mathrm{virus\_total}}{1}\right)$