kirschner1

The model reproduces Fig 2 of the paper.

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Title

Immunotherapy of HIV-1 infection.

Authors

Denise E. Kirschner (1) and G. F. Webb (2)

Affiliations

1) Department of Microbiology and Immunology, University of Michigan Medical School, Ann Arbor, MI 48109-0620, USA. 2) Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA.

Abstract

A number of lines of evidence suggest that immunotherapy with the cytokine interleukin-2 (IL-2) may boost the immune response to fight HIV infection. CD4+ T cells, the cells which orchestrate the immune response, are also the cells that become infected by the HIV virus. These cells use cytokines as signaling mechanisms for immune-response stimulation, growth and differentiation. Since CD4+ T cells are hampered due to HIV infection, normal signaling, and the resulting cascade, may not occur. Introduction of IL-2 into the system can restore or enhance these effects. We illustrate, through mathematical modeling, the effects of IL-2 treatment on an HIV-infected patient. With good comparison to existing clinical data, we can better understand what mechanisms of immune-viral dynamics are necessary to produce the typical disease dynamics.

Journal

Journal of Biological Systems, Vol. 6, No. 1 (1998) 71-83

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
default 1.0
Id Name Initial quantity Compartment Fixed
T 1000.0 default
V 3.0 default

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
v1 ∅ = T

s1
v2 T = ∅

(s2*V)/(b1 + V)
v3 T = ∅

mu*T
v4 T = ∅

k*T*V
v5 ∅ = V

(g*V)/(b2 + V)
v6 V = ∅

c*T*V

Global parameters

Id Value
VMULTIPLIED 0.0
b1 14.0
b2 1.0
c 0.007
g 30.0
k 0.00025
mu 0.002
s1 2.0
s2 1.5

Local parameters

Id Value Reaction

Assignment rules

Definition
VMULTIPLIED = 1000.0*V

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments