Influence of Delayed Viral Production on Viral Dynamics in HIV-1 Infected Patients
Catherine
Lloyd
Auckland Bioengineering Institute, The University of Auckland
Model Status
This CellML model runs in both OpenCell and COR however we are uncertain as to whether or not the CellML model replicates the original model from the published paper as there are no validation figures to compare it against. The CellML model is based on equatiosn 10a to 10e. Parameter values for the variables k and p are not stated in the paper so in the CellML model these were taken from a previously published model by the same author (Perelson et al. 1996). The units have been checked and they are consistent. Note that while the model does run in COR, since the unit of time is days the model is not ideally suited for running in COR.
Model Structure
ABSTRACT: We present and analyze a model for the interaction of human immunodeficiency virus type 1 (HIV-1) with target cells that includes a time delay between initial infection and the formation of productively infected cells. Assuming that the variation among cells with respect to this 'intracellular' delay can be approximated by a gamma distribution, a high flexible distribution that can mimic a variety of biologically plausible delays, we provide analytical solutions for the expected decline in plasma virus concentration after the initiation of antiretroviral therapy with one or more protease inhibitors. We then use the model to investigate whether the parameters that characterize viral dynamics can be identified from biological data. Using non-linear least-squares regression to fit the model to simulated data in which the delays conform to a gamma distribution, we show that good estimates for free viral clearance rates, infected cell death rates, and parameters characterizing the gamma distribution can be obtained. For simulated data sets in which the delays were generated using other biologically plausible distributions, reasonably good estimates for viral clearance rates, infected cell death rates, and mean delay times can be obtained using the gamma-delay model. For simulated data sets that include added simulated noise, viral clearance rate estimates are not as reliable. If the mean intracellular delay is known, however, we show that reasonable estimates for the viral clearance rate can be obtained by taking the harmonic mean of viral clearance rate estimates from a group of patients. These results demonstrate that it is possible to incorporate distributed intracellular delays into existing models for HIV dynamics and to use these refined models to estimate the half-life of free virus from data on the decline in HIV-1 RNA following treatment.
The original paper reference is cited below:
Influence of Delayed Viral Production on Viral Dynamics in HIV-1 Infected Patients, John E. Mittler, Bernhard Sulzer, Avidan U. Neumann, and Alan S. Perelson, 1998, Mathematical Biosciences
, 152, 143-163. PubMed ID: 9780612
cell diagram
Schematic summary of the dynamics of HIV-1 infection in vivo captured by the Perelson et al. 1996 model.
cell diagram
Schematic summary of the dynamics of viral infection in vivo captured by the Herz et al. 1996 model.
T
uninfected target CD4 cells
I
productively infected cells
VI
infectious virus
VNI
non-infectious virus
viral dynamics
hiv-1
immunology
Influence of delayed viral production on viral dynamics in HIV-1
infected patients
152
143
163
Bernhard
Sulzer
c.lloyd@auckland.ac.nz
1998-09
Avidan
Neumann
U
Catherine
Lloyd
May
Mathematical Biosciences
Alan
Perelson
S
keyword
This is the CellML description of Mittler et al.'s 1998 mathematical
model of the influence of delayed viral production on viral dynamics
in HIV-1 infected patients.
2003-12-05
Catherine Lloyd
The University of Auckland
Auckland Bioengineering Institute
John
Mittler
E
The University of Auckland, Auckland Bioengineering Institute
9780612
Mittler et al.'s 1998 mathematical model of the influence of delayed
viral production on viral dynamics in HIV-1 infected patients.
$T=\frac{c\mathrm{delta}}{kp}$
$\frac{d I}{d \mathrm{time}}=\mathrm{k\_}T\mathrm{E4}-\mathrm{delta}I\mathrm{I\_0}=\frac{c}{p}\mathrm{VI\_0}$
$\frac{d \mathrm{VI}}{d \mathrm{time}}=(1-h)pI-c\mathrm{VI}$
$\frac{d \mathrm{VNI}}{d \mathrm{time}}=hpI-c\mathrm{VNI}$
$V=\mathrm{VI}+\mathrm{VNI}$
$\frac{d \mathrm{E1}}{d \mathrm{time}}=\frac{\mathrm{VI}-\mathrm{E1}}{\mathrm{b\_}}$
$\frac{d \mathrm{E2}}{d \mathrm{time}}=\frac{\mathrm{E1}-\mathrm{E2}}{\mathrm{b\_}}$
$\frac{d \mathrm{E3}}{d \mathrm{time}}=\frac{\mathrm{E2}-\mathrm{E3}}{\mathrm{b\_}}$
$\frac{d \mathrm{E4}}{d \mathrm{time}}=\frac{\mathrm{E3}-\mathrm{E4}}{\mathrm{b\_}}$
$h=\begin{cases}0 & \text{if $\mathrm{time}< \mathrm{tau\_p}$}\\ 1 & \text{otherwise}\end{cases}$
$\mathrm{b\_}=\frac{b}{1+mb}\mathrm{k\_}=\frac{k}{(1+mb)^{n}}$