Abstract:

In this paper, an HTLV-I infection model with delayed and saturated CTL immune response and immune impairment is developed. By calculations, the existences of feasible equilibria are established, immunity-inactivated and immunity-activated reproduction ratios are also derived. Under the assistance of proper Lyapunov functionals and LaSalle's invariance principle, it is shown that the infection-free equilibrium is globally asymptotically stable if the immunity-inactivated reproduction ratio is less than unity; the immunity-inactivated equilibrium is globally asymptotically stable if the immunity-activated reproduction ratio is less than unity, while the immunity-inactivated reproduction ratio is greater than unity; the immunity-activated equilibrium is globally asymptotically stable (when the time delay equals to zero) if the immunity-activated reproduction ratio is greater than unity. A Hopf bifurcation at the immunity-activated equilibrium occurs as the time delay crosses a critical value. Finally, numerical simulations are performed to illustrate the theoretical results.

Key words: HTLV-I infection, Immune delay, Saturated CTL immune response, Immune impairment, Hopf bifurcation