  GRB 080503, detected by Swift, belongs to the class of bursts whose prompt
phase consists of an initial short spike followed by a longer soft tail. It did
not show any transition to a regular afterglow at the end of the prompt
emission but exhibited a surprising rebrightening after one day. We aim to
explain this rebrightening with two different scenarios - refreshed shocks or a
density clump in the circumburst medium - and two models for the origin of the
afterglow, the standard one where it comes from the forward shock, and an
alternative one where it results from a long-lived reverse shock. We computed
afterglow light curves either using a single-zone approximation for the shocked
region or a detailed multizone method that more accurately accounts for the
compression of the material. We find that in several of the considered cases
the detailed model must be used to obtain a reliable description of the shock
dynamics. The density clump scenario is not favored. We confirm previous
results that the presence of the clump has little effect on the forward shock
emission, except if the microphysics parameters evolve when the shock enters
the clump. Moreover, we find that the rebrightening from the reverse shock is
also too weak when it is calculated with the multi-zone method. On the other
hand, in the refreshed-shock scenario both the forward and reverse shock models
provide satisfactory fits of the data under some additional conditions on the
distribution of the Lorentz factor in the ejecta and the beaming angle of the
relativistic outflow.
