A stochastic spatial model for the sterile insect control strategy

In the system we study, 1s and 0s 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 $thetaalpha$. 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 $alphato 0$. In this regime the process resembles the contact process in a random environment.