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Global analysis for delay virus dynamics model with Beddington-DeAngelis functional response. (English) Zbl 1217.34128
Summary: A class of virus dynamics model with intracellular delay and nonlinear infection rate of Beddington-DeAngelis functional response is analysed in this paper. By constructing suitable Lyapunov functionals and using a LaSalle-type theorem for delay differential equations, we show that the global stability of the infection-free equilibrium and the infected equilibrium depends on the basic reproductive ratio ${R}_{0}$, that is, the former is globally stable if ${R}_{0}\le 1$ and so is the latter if ${R}_{0}>1$. Our results extend known results on delay virus dynamics and suggest useful methods to control virus infection.
##### MSC:
 34K60 Qualitative investigation and simulation of models 34K20 Stability theory of functional-differential equations 92D30 Epidemiology