Modeling defective interfering virus therapy for AIDS: conditions for DIV survival
Ethan
Choi
Auckland Bioengineering Institute, The University of Auckland
Model Status
This model has been built with the differential expressions in Nelson and Perelson's 1995 paper for the model with DIV interference (equations 1-3, and 7-13). This file is known to run in OpenCell and COR, and uses the parameters values in Tables 1, 2, and 3 of the paper. One of the units (for the variable theta) has been changed from micro_L (in the paper), to per_micro_L, to be dimensionally consistent. Parameters in years are represented in day equivalents. In order to model the inoculum of DIV (an ODE that must have an initial condition at a certain time), a function was created to get the value up to the initial condition, then swapped out via a piecewise.
Model Structure
ABSTRACT: The administration of a genetically engineered defective interfering virus (DIV) that interferes with HIV-1 replication has been proposed as a therapy for HIV-1 infection and AIDS. The proposed interfering virus, which is designed to superinfect HIV-1 infected cells, carries ribozymes that cleave conserved regions in HIV-1 RNA that code for the viral envelope protein. Thus DIV infection of HIV-1 infected cells should reduce or eliminate viral production by these cells. The success of this therapeutic strategy will depend both on the intercellular interaction of DIV and HIV-1, and on the overall dynamics of virus and T cells in the body. To study these dynamical issues, we have constructed a mathematical model of the interaction of HIV-1, DIV, and CD4+ cells in vivo. The results of both mathematical analysis and numerical simulation indicate that survival of the engineered DIV purely on a peripheral blood HIV-1 infection is unlikely. However, analytical results indicate that DIV might well survive on HIV-1 infected CD4+ cells in lymphoid organs such as lymph nodes and spleen, or on other HIV-1 infected cells in these organs.
model diagram
Schematic illustration of the main features of the model.
The original paper reference is cited below:
Modeling defective interfering virus therapy for AIDS: conditions for DIV survival, Nelson G, Perelson A, 1995, Mathematical Biosciences, 125, 127-153. PubMed ID: 7881191
$\frac{d T}{d \mathrm{time}}=\mathrm{s\_V}-\mathrm{mu\_T}T+rT(1-\frac{T+\mathrm{T\_1}}{\mathrm{T\_max}})-\mathrm{k\_1}VT-\mathrm{k\_1\_}\mathrm{V\_}T\mathrm{s\_V}=\frac{\mathrm{s\_0}\mathrm{theta}}{\mathrm{theta}+V}$
$\frac{d \mathrm{T\_1}}{d \mathrm{time}}=\mathrm{k\_1}VT+\mathrm{k\_1\_}\mathrm{V\_}T-\mathrm{mu\_T}\mathrm{T\_1}-\mathrm{k\_2}\mathrm{T\_1}$
$\frac{d \mathrm{T\_2}}{d \mathrm{time}}=\mathrm{k\_2}\mathrm{T\_1}-\mathrm{k\_1D}D\mathrm{T\_2}-\mathrm{mu\_b}\mathrm{T\_2}$
$\frac{d \mathrm{T\_D2}}{d \mathrm{time}}=\mathrm{k\_1D}D\mathrm{T\_2}-\mathrm{k\_s}\mathrm{T\_D2}-\mathrm{mu\_bD}\mathrm{T\_D2}$
$\frac{d \mathrm{T\_D1}}{d \mathrm{time}}=\mathrm{k\_s}\mathrm{T\_D2}-\mathrm{mu\_TD}\mathrm{T\_D1}$
$D=\begin{cases}0 & \text{if $\mathrm{time}< \mathrm{t\_DIV}$}\\ \mathrm{D\_ode} & \text{otherwise}\end{cases}\frac{d \mathrm{D\_ode}}{d \mathrm{time}}=\begin{cases}\frac{\mathrm{D\_0}}{\mathrm{t\_DIV}} & \text{if $\mathrm{time}< \mathrm{t\_DIV}$}\\ \mathrm{N\_D\_t}\mathrm{mu\_bD}\mathrm{T\_D2}+\mathrm{pi\_D\_t}\mathrm{T\_D1}-\mathrm{mu\_D}\mathrm{D\_ode} & \text{otherwise}\end{cases}\mathrm{N\_D\_t}=0.2\mathrm{N\_t}\mathrm{pi\_D\_t}=0.5\mathrm{mu\_b}\mathrm{N\_t}$
$\frac{d V}{d \mathrm{time}}=\mathrm{N\_t}\mathrm{mu\_b}\mathrm{T\_2}+\mathrm{N\_2\_t}\mathrm{mu\_bD}\mathrm{T\_D2}-\mathrm{k\_1}VT-\mathrm{mu\_V}V\mathrm{N\_2\_t}=0.1\mathrm{N\_t}$
$\frac{d \mathrm{V\_}}{d \mathrm{time}}=\mathrm{N\_t\_}\mathrm{mu\_bD}\mathrm{T\_D2}+\mathrm{pi\_t\_}\mathrm{T\_D1}-\mathrm{mu\_V}\mathrm{V\_}-\mathrm{k\_1\_}T\mathrm{V\_}\mathrm{N\_t\_}=0.1\mathrm{N\_t}\mathrm{pi\_t\_}=0.01\mathrm{mu\_b}\mathrm{N\_t}$
$\mathrm{N\_t}=\mathrm{N\_0}(1+\mathrm{gamma}\frac{\mathrm{time}^{2}}{\mathrm{time}^{2}+\mathrm{t\_c}^{2}})$
$\mathrm{T\_tot}=T+\mathrm{T\_1}+\mathrm{T\_2}+\mathrm{T\_D2}+\mathrm{T\_D1}$
Modeling defective interfering virus therapy for AIDS: conditions for DIV survival (DIV Interference)
Choi
Ethan
mcho099@aucklanduni.ac.nz
The University of Auckland
Auckland Bioengineering Institute
2010-01-26
Modeling defective interfering virus therapy for AIDS: conditions for DIV survival
This is the CellML description of Nelson and Perelson's 1995 mathematical model for a defective interfering virus therapy for AIDS
Ethan Choi
CD4+ T cell
Keywords
Immunology
CD4 T cell
HIV-1
dynamics
DIV
engineered virus
7881191
Nelson
George
W
Perelson
Alan
S
Modeling defective interfering virus therapy for AIDS: conditions for DIV survival
1995-02
Mathematical Biosciences
125
127
153
4383
100000