  We study extended infection fronts advancing over a spatially uniform
susceptible population by solving numerically a diffusive Kermack McKendrick
SIR model with a dichotomous spatially random transmission rate, in two
dimensions. We find a non-trivial dynamic critical behavior in the mean
velocity, in the shape, and in the rough geometry of the displacement field of
the infective front as the disorder approaches a threshold value for spatial
spreading of the infection.
