  The effect of continuum couplings in the fusion of the halo nucleus $^{11}$Be
on $^{208}$Pb around the Coulomb barrier is studied using a three-body model
within a coupled discretised continuum channels (CDCC) formalism. We
investigate in particular the role of continuum-continuum couplings. These are
found to hinder total, complete and incomplete fusion processes. Couplings to
the projectile $1p_{1/2}$ bound excited state redistribute the complete and
incomplete fusion cross sections, but the total fusion cross section remains
nearly constant. Results show that continuum-continuum couplings enhance the
irreversibility of breakup and reduce the flux that penetrates the Coulomb
barrier. Converged total fusion cross sections agree with the experimental ones
for energies around the Coulomb barrier, but underestimate those for energies
well above the Coulomb barrier.
