Driving biofilms to finite time extinction by antibiotic cocktails

Abstract

Hospital acquired infections are often caused by biofilms growing on medical devices and implants. Biofilms are bacterial aggregates attached to wet surfaces that are glued together by a self-produced polymeric matrix. Devising protocols and therapies able to eradicate biofilms in medical environments is essential to prevent chronic infections, implant removal and sepsis. We present a simple model of combined antibiotic action which leads to extinction of a biofilm system in finite time. Slow death rates growing like powers φ γ, 0 < γ < 1, are key to achieve extinction. The model combines a nonlocal nonlinear transport equation with a quasi-stationary reaction-diffusion system, all set in a domain whose boundary moves with time. Estimates of extinction times suggest therapies based on administering large enough doses for a long enough time, or periodically for shorter times, validated by numerical simula tions and theoretical results. Furthermore, we devise bang-bang and optimal control strategies based on Bucy-Kalman filters to achieve biofilm extinction in a given time through adequate antibiotic dosage. Interestingly, lower dosages with and abrupt final increase seem to suffice.