  In the system we study, 1's and 0's represent occupied and vacant sites in
the contact process with births at rate $\lambda$ and deaths at rate 1. $-1$'s
are sterile individuals that do not reproduce but appear spontaneously on
vacant sites at rate $\alpha$ and die at rate $\theta\alpha$. We show that the
system (which is attractive but has no dual) dies out at the critical value and
has a nontrivial stationary distribution when it is supercritical. Our most
interesting results concern the asymptotics when $\alpha\to 0$. In this regime
the process resembles the contact process in a random environment.
