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

TL;DR

This paper derives the macroscopic hydrodynamic and hydrostatic limits of a generalized contact process modeling sterile insect techniques, revealing coupled reaction-diffusion equations with mixed boundary conditions.

Contribution

It establishes the hydrodynamic and hydrostatic limits for a generalized contact process with mixed boundary conditions, extending previous models.

Findings

Hydrodynamic limit is a set of coupled nonlinear reaction-diffusion equations.

Hydrostatic limit is characterized when the macroscopic system has a unique attractor.

Results apply to systems with reservoirs at different slowdown rates.

Abstract

We consider an interacting particle system which models the sterile insect technique. It is the superposition of a generalized contact process with exchanges of particles on a finite cylinder with open boundaries (see Kuoch et al., 2017). We show that when the system is in contact with reservoirs at different slowdown rates, the hydrodynamic limit is a set of coupled non linear reaction-diffusion equations with mixed boundary conditions. We also prove the hydrostatic limit when the macroscopic equations exhibit a unique attractor.