  Although it is well recognized that gamma-ray burst (GRB) afterglows are
obscured and reddened by dust in their host galaxies, the wavelength-dependence
and quantity of dust extinction are still poorly known. Current studies on this
mostly rely on fitting the afterglow spectral energy distributions (SEDs) with
template extinction models. The inferred extinction (both quantity and
wavelength-dependence) and dust-to-gas ratios are often in disagreement with
that obtained from dust depletion and X-ray spectroscopy studies. We argue that
this discrepancy could result from the prior assumption of a template
extinction law. We propose an analytical formula to approximate the GRB host
extinction law. With the template extinction laws self-contained, and the
capability of revealing extinction laws differing from the conventional ones,
it is shown that this is a powerful approach in modeling the afterglow SEDs to
derive GRB host extinction.
