%0 Journal Article
%A Birnir, B.
%A Carpio Rodríguez, Ana María
%A Duro, G.
%T Driving biofilms to finite time extinction by antibiotic cocktails
%D 2025
%U https://hdl.handle.net/20.500.14352/124692
%X 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.
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