Modelling Viral Dynamics In Vivo
Catherine
Lloyd
Bioengineering Institute, University of Auckland
Model Status
This model contains time delays and is unsuitable for solution using CellML. There are additional problems with the model, but the presence of time delays rendered these superfluous.
Model Structure
Clinical studies of drug therapy in patients infected with HIV-1 or the hepatitis B virus provide the opportunity for estimating the kinetic constants of virus replication in vivo. Treatment of HIV-1 with protease inhibitors results in the decline of free virus in several distinct phases: Initially the plasma virus load remains virtually unchanged, then after this initial delay, the plasma load declines exponentially, due to the decreased virus synthesis in infected cells, and also due to the clearance of free virus particles. Finally, the rate of virus decline decreases, and the viral load may even begin to increase again as the virus evolves a resistance to the protease inhibitor.
This publication by Herz et al. quickly followed an article by Perelson et al. (1996) in which they developed a mathematical model of HIV-1 dynamics in vivo based on their experimental data. In this current publication, Herz et al. develop a new model that provides a description of HIV-1 dynamics, including the effects of an intracellular delay (the period between infection of a cell and the production of new virus particles). This model accounts for the effects of a protease inhibitor on the rate of viral synthesis (see below), and it has been encoded in CellML and can be downloaded in various formats in .
The complete original paper reference is cited below:
Limitations on estimates of intracellular delay and virus decay, Andreas V. M. Herz, Sebastian Bonhoeffer, Roy M. Anderson, Robert M. May, and Martin A. Nowak, 1996, Proceedings of the National Academy of Science, USA, 93, 7247-7251. PubMed ID: 8692977
cell diagram
Schematic summary of the dynamics of viral infection in vivo.
Model simulations revealed that the half-life of the infected cells can be calculated with reasonable accuracy from clinical data. However, the remaining parameters can not be accurately predicted from the current model, more data is needed.
x
uninfected cells
$\frac{d x}{d \mathrm{time}}=\mathrm{lamda}-x+\mathrm{beta}x\mathrm{vI}$
y
virus producing infected cells
$\frac{d y}{d \mathrm{time}}=\mathrm{beta}(\mathrm{time}-\mathrm{tau})x(\mathrm{time}-\mathrm{tau})\mathrm{vI}(\mathrm{time}-\mathrm{tau})e^{\mathrm{a\_}\mathrm{tau}}-ay$
v
plasma virus
$\frac{d v}{d \mathrm{time}}=ky-uv$
vI
infectious plasma virus
$\frac{d \mathrm{vI}}{d \mathrm{time}}=-(u\mathrm{vI})$
immunology
viral dynamics
Proceedings of the National Academy of Science, USA
Viral Dynamics in vivo: Limitations on estimates of intracellular delay and virus decay
93
7247
7251
2003-12-03
Catherine
Lloyd
May
Roy
Anderson
M
Sebastian
Bonhoeffer
c.lloyd@auckland.ac.nz
8692977
Martin
Nowak
A
The University of Auckland, Bioengineering Institute
Herz et al.'s 1996 mathematical model of viral dynamics in vivo.
This is the CellML description of Herz et al.'s 1996 mathematical model of viral dynamics in vivo.
keyword
Andreas
Herz
M
V
Robert
May
M
Catherine Lloyd
1996-07-09
The University of Auckland
The Bioengineering Institute