  We investigate the propagating profiles of a degenerate chemotaxis model
describing the bacteria chemotaxis and consumption of oxygen by aerobic
bacteria, in particular, the effect of the initial attractant distribution on
bacterial clustering. We prove that the compact support of solutions may shrink
if the signal concentration satisfies a special structure, and show the finite
speed propagating property without assuming the special structure on attractant
concentration, and obtain an explicit formula of the population spreading speed
in terms of model parameters. The presented results suggest that bacterial
cluster formation can be affected by chemotactic attractants and
density-dependent dispersal.
