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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 A. S. Perelson and P. W. Nelson [SIAM Rev. 41, 3–44 (1999; Zbl 1078.92502)] and M. A. Nowak and 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.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
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