  The contact process is a stochastic process which exhibits a continuous,
absorbing-state phase transition in the Directed Percolation (DP) universality
class. In this work, we consider a contact process with a bias in conjunction
with an active wall. This model exhibits waves of activity emanating from the
active wall and, when the system is supercritical, propagating indefinitely as
travelling (Fisher) waves. In the subcritical phase the activity is localised
near the wall. We study the phase transition numerically and show that certain
properties of the system, notably the wave velocity, are discontinuous across
the transition. Using a modified Fisher equation to model the system we
elucidate the mechanism by which the the discontinuity arises. Furthermore we
establish relations between properties of the travelling wave and DP critical
exponents.
