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Impact of intracellular delays and target-cell dynamics on in vivo viral infections. (English) Zbl 1209.92037

Summary: The dynamics of an in-host model with general form of target-cell dynamics, nonlinear incidence, and distributed delay are investigated. The model can describe the in vivo infection dynamics of many viruses such as HIV-I, HCV, and HBV. We derive the basic reproduction number \(R_{0}\) for the viral infection and establish that the global dynamics are completely determined by the values of \(R_{0}\): if \(R_{0}\leq 1\), the infection-free equilibrium is globally asymptotically stable, and the virus is cleared; if \(R_{0}>1\), then the infection persists, and the chronic-infection equilibrium is globally asymptotically stable. An implication of our results is that intracellular delays will lead to periodic oscillations in in-host models only with the right kind of target-cell dynamics.

MSC:

92C60 Medical epidemiology
34D23 Global stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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