Birnir, B.Carpio Rodríguez, Ana MaríaDuro, G.2025-10-092025-10-09202510.1016/j.cnsns.2025.109362https://hdl.handle.net/20.500.14352/124692Acuerdos transformativos CRUE 2025Hospital 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/journal articleopen accessAntiobiotic treatmentFinite time extinctionNonlinear controlTransport-reaction-diffusion coupled systemsMatemáticas (Matemáticas)Biomatemáticas2404 Biomatemáticas