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In the present paper we propose a bi-dimensional non-linear reaction-diffusion model describing the action of antibiotics as well as quorum sensing inhibitors agents on the virulence of bacteria biofilms. We thus approximate the system by a standard finite element scheme in space and an implicit Euler method in time. We prove the existence and uniqueness of a solution to this system and prove its convergence to a weak solution of the model we introduce. We present numerical results fordoi:10.1051/proc/201862017 fatcat:karx2rprj5ec3b7yuwoyzxyqzu