Dynamical behaviour of a delay differential equation of Hepatitis B virus

In this paper, we investigate a class of virus dynamics model with intracellular delay and nonlinear infection rate of saturated functional response. The basic reproduction number R₀ for the viral infection is derived, and the global dynamics behavior are completely determined by R₀. By constructing suitable Lyapunov functional and using LaSalle invariant principle for the delay differential equations, we find when R₀ ≤ 1, the infection-free equilibrium is globally asymptotically stable, and when R₀ > 1, the infection equilibrium is also globally asymptotically stable.