Abstract
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≤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 functional, 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.
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Li, M.Y., Shu, H. Global Dynamics of an In-host Viral Model with Intracellular Delay. Bull. Math. Biol. 72, 1492–1505 (2010). https://doi.org/10.1007/s11538-010-9503-x
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DOI: https://doi.org/10.1007/s11538-010-9503-x