Li, Michael Y.; Shu, Hongying Impact of intracellular delays and target-cell dynamics on in vivo viral infections. (English) Zbl 1209.92037 SIAM J. Appl. Math. 70, No. 7, 2434-2448 (2010). 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. Cited in 90 Documents MSC: 92C60 Medical epidemiology 34D23 Global stability of solutions to ordinary differential equations 34D05 Asymptotic properties of solutions to ordinary differential equations Keywords:in-host models; target-cell dynamics; intracellular delays; periodic oscillations; global stability; Lyapunov functionals PDFBibTeX XMLCite \textit{M. Y. Li} and \textit{H. Shu}, SIAM J. Appl. Math. 70, No. 7, 2434--2448 (2010; Zbl 1209.92037) Full Text: DOI Link