Using this simple model we show that many of the puzzling quantitative features of HIV infection can simply be explained. We also rigorously examine many of the model's features that were previously explored through simulation. We also consider new aspects, such as the effects of AZT on viral growth and T cell population dynamics. If the endemically infected state is unstable, we find that it is surrounded by a stable limit cycle. Using numerical birfurcation techniques we map out the parameter regimes of these various behaviors.
Oscillatory behavior seems to lie outside the region of biologically releastic parameter values.
When the endemically infected state is stable, it is characterized by a reduced number of T cells when compared with the uninfected state. Thus T cell depletion occurs through the establishment of a new steady state. The dynamics of the establishment of this new steady state is examined both numerically and via the quasi-steady state approximation. We develop approximations for the dynamics at early times, in which the free virus rapidly binds to T cells, during an intermediate time scale in which the virus grows exponentially, and then a third time scale on which viral growth slows and the endemically infected steady state is approached. We compute the level of T cells in the endemically infected state, and show how that level varies with the parameters in the model.