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Global dynamics of an in-host viral model with intracellular delay. (English) Zbl 1198.92034
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.

92C60Medical epidemiology
34D05Asymptotic stability of ODE
34D23Global stability of ODE
92C50Medical applications of mathematical biology
37N25Dynamical systems in biology
Full Text: DOI
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