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Zbl 1209.92037
Li, Michael Y.; Shu, Hongying
Impact of intracellular delays and target-cell dynamics on in vivo viral infections. (English)
[J] SIAM J. Appl. Math. 70, No. 7, 2434-2448 (2010). ISSN 0036-1399; ISSN 1095-712X/e

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 2000:: *92C60 Medical epidemiology
34D23 Global stability
34D05 Asymptotic stability of ODE

Keywords: in-host models; target-cell dynamics; intracellular delays; periodic oscillations; global stability; Lyapunov functionals

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Zentralblatt MATH Berlin [Germany]