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We consider an interacting particle system which models the sterile insecttechnique. It is the superposition of a generalized contact process withexchanges of particles on a finite cylinder with open boundaries (see Kuoch etal., 2017). We show that when the system is in contact with reservoirs atdifferent slowdown rates, the hydrodynamic limit is a set of coupled non linearreaction-diffusion equations with mixed boundary conditions. We also prove thehydrostatic limit when the macroscopic equations exhibit a unique attractor.

Hydrodynamic and hydrostatic limit for a generalized contact process with mixed boundary conditions