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Zbl 1198.92034
Li, Michael Y.; Shu, Hongying
Global dynamics of an in-host viral model with intracellular delay. (English)
[J] Bull. Math. Biol. 72, No. 6, 1492-1505 (2010). ISSN 0092-8240; ISSN 1522-9602/e

Summary: The dynamics of a general in-host model with intracellular delay is studied. The model can describe in vivo infections of HIV-I, HCV, and HBV. It can also be considered as a model for HTLV-I infection. 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 are cleared. If $R _{0} > 1$, then the infection persists and the chronic-infection equilibrium is locally asymptotically stable. Furthermore, using the method of Lyapunov functionals, we prove that the chronic-infection equilibrium is globally asymptotically stable when $R _{0} >1$. Our results shows that for intercellular delays to generate sustained oscillations in in-host models it is necessary have a logistic mitosis term in target-cell compartments.

MSC 2000:: *92C60 Medical epidemiology
34D05 Asymptotic stability of ODE
34D23 Global stability
92C50 Medical appl. of mathematical biology
37N25 Dynamical systems in biology

Keywords: in-host models; intracellular delays; global stability; Lyapunov functionals

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Zentralblatt MATH Berlin [Germany]