  We study the diffusive escape of cosmic rays from a central source inside a
galaxy cluster to obtain the suppression in the outgoing flux appearing when
the confinement times get comparable or larger than the age of the sources. We
also discuss the attenuation of the flux due to the interactions of the cosmic
rays with the cluster medium, which can be sizeable for heavy nuclei. The
overall suppression in the total cosmic ray flux expected on Earth is important
to understand the shape of the extragalactic contribution to the cosmic ray
spectrum for $E/Z<1$ EeV. This suppression can also be relevant to interpret
the results of fits to composition-sensitive observables measured at ultra-high
energies.
