Exploiting the fact that standard models of within-host viral infections of target cell populations by HIV, developed by Perelson and Nelson [SIAM Rev., 41 (1999), pp. 3--44] and Nowak and May [Virus Dynamics, Oxford University Press, New York, 2000], give rise to competitive three dimensional dynamical systems, we provide a global analysis of their dynamics. If the basic reproduction number R0 < 1, the virus is cleared and the disease dies out; if R0 > 1, then the virus persists in the host, solutions approaching either a chronic disease steady state or a periodic orbit. The latter can be ruled out in some cases but not in general.
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Smith et al. (2003) studied this question.
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