  We study a one-dimensional contact process with two infection parameters. One
giving the infection rates at the boundaries of a finite infected region and
the other one the rates within that region. We prove that the critical value of
each of these parameters is a strictly monotone continuous function of the
other parameter. We also show that if one of these parameters is equal to the
critical value of the standard contact process and the other parameter is
strictly larger, then the infection starting from a single point has positive
probability of surviving.
