  We study travelling-wave solutions for a reaction-diffusion system arising as
a model for host-tissue degradation by bacteria. This system consists of a
parabolic equation coupled with an ordinary differential equation. For large
values of the `degradation-rate parameter' solutions are well approximated by
solutions of a Stefan-like free boundary problem, for which travelling-wave
solutions can be found explicitly. Our aim is to prove the existence of
travelling waves for all sufficiently large wave-speeds for the original
reaction-diffusion system and to determine the minimal speed. We prove that for
all sufficiently large degradation rates the minimal speed is identical to the
minimal speed of the limit problem. In particular, in this parameter range,
nonlinear selection of the minimal speed occurs.
