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Virus dynamics: A global analysis. (English) Zbl 1035.34045
Summary: Exploiting the fact that standard models of within-host viral infections of target cell populations by HIV, developed by {\it A. S. Perelson} and {\it P. W. Nelson} [SIAM Rev. 41, 3--44 (1999; Zbl 1078.92502)] and {\it M. A. Nowak} and {\it R. M. May} [Virus dynamics. Mathematical principles of immunology and virology. Oxford: Oxford University Press (2000; Zbl 1101.92028)], give rise to competitive three-dimensional dynamical systems, we provide a global analysis of their dynamics. If the basic reproduction number $R_{0}<1$, the virus is cleared and the disease dies out; if $R_{0}>1$, 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.

34C60Qualitative investigation and simulation of models (ODE)
34D23Global stability of ODE
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