Global dynamics of a delayed HTLV-I infection model with Beddington-DeAngelis incidence and immune impairment

Abstract

In this paper, we investigate a delayed HTLV-I infection model with Beddington-DeAngelis incidence, CTL immune response and immune impairment. In the model, the intracellular delay and immune response delay are considered. By calculation, we obtain the basic reproductive ratio. By analyzing corresponding characteristic equations, the local stabilities of feasible equilibria are established. By using Lyapunov functionals and LaSalle’s invariance principle, it is shown that when the basic reproductive ratio is less than or equal to unity, the infection-free equilibrium is globally asymptotically stable. When the basic reproductive ratio is greater than unity and immune response delay is equal to zero, the chronic-infection equilibrium is globally asymptotically stable. When the basic reproductive ratio is greater than unity and the intracellular delay is equal to zero, immune response delay will destabilize stability and lead to Hopf bifurcation. Numerical simulations are carried out to illustrate the theoretical results.