This a model from the article:
Dynamics of HIV infection of CD4+ T cells.
Perelson AS, Kirschner DE, De Boer R. Math Biosci 1993 Mar;114(1):81-125 8096155 ,
Abstract:
We examine a model for the interaction of HIV with CD4+ T cells that considersfour populations: uninfected T cells, latently infected T cells, activelyinfected T cells, and free virus. Using this model we show that many of thepuzzling quantitative features of HIV infection can be explained simply. We alsoconsider effects of AZT on viral growth and T-cell population dynamics. Themodel exhibits two steady states, an uninfected state in which no virus ispresent and an endemically infected state, in which virus and infected T cellsare present. We show that if N, the number of infectious virions produced peractively infected T cell, is less a critical value, Ncrit, then the uninfectedstate is the only steady state in the nonnegative orthant, and this state isstable. For N > Ncrit, the uninfected state is unstable, and the endemicallyinfected state can be either stable, or unstable and surrounded by a stablelimit cycle. Using numerical bifurcation techniques we map out the parameterregimes of these various behaviors. oscillatory behavior seems to lie outsidethe region of biologically realistic parameter values. When the endemicallyinfected state is stable, it is characterized by a reduced number of T cellscompared with the uninfected state. Thus T-cell depletion occurs through theestablishment of a new steady state. The dynamics of the establishment of thisnew steady state are examined both numerically and via the quasi-steady-stateapproximation. We develop approximations for the dynamics at early times inwhich the free virus rapidly binds to T cells, during an intermediate time scalein which the virus grows exponentially, and a third time scale on which viralgrowth slows and the endemically infected steady state is approached. Using thequasi-steady-state approximation the model can be simplified to two ordinarydifferential equations the summarize much of the dynamical behavior. We computethe level of T cells in the endemically infected state and show how that levelvaries with the parameters in the model. The model predicts that different viralstrains, characterized by generating differing numbers of infective virionswithin infected T cells, can cause different amounts of T-cell depletion andgenerate depletion at different rates. Two versions of the model are studied. Inone the source of T cells from precursors is constant, whereas in the other thesource of T cells decreases with viral load, mimicking the infection and killingof T-cell precursors.(ABSTRACT TRUNCATED AT 400 WORDS)

This model was taken from the CellML repository and automatically converted to SBML.
The original model was: Perelson AS, Kirschner DE, De Boer R. (1993) - version=1.0
The original CellML model was created by:
Ethan Choi
mcho099@aucklanduni.ac.nz
The University of Auckland

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