Bull Math Biol DOI 10.1007/s11538-011-9698-5 ORIGINAL ARTICLE Selecting Against Antibiotic-Resistant Pathogens: Optimal Treatments in the Presence of Commensal Bacteria Rafael Peña-Miller · David Lähnemann · Hinrich Schulenburg · Martin Ackermann · Robert Beardmore Received: 12 May 2011 / Accepted: 6 October 2011 © Society for Mathematical Biology 2011 Abstract Using optimal control theory as the basic theoretical tool, we investigate the efficacy of different antibiotic treatment protocols in the most exacting of circum- stances, described as follows. Viewing a continuous culture device as a proxy for a much more complex host organism, we first inoculate the device with a single bac- terial species and deem this the ‘commensal’ bacterium of our host. We then force the commensal to compete for a single carbon source with a rapidly evolving and fitter ‘pathogenic bacterium’, the latter so-named because we wish to use a bacterio- static antibiotic to drive the pathogen toward low population densities. Constructing a mathematical model to mimic the biology, we do so in such a way that the commensal would be eventually excluded by the pathogen if no antibiotic treatment were given to the host or if the antibiotic were over-deployed. Indeed, in our model, all fixed-dose antibiotic treatment regimens will lead to the eventual loss of the commensal from the host proxy. Despite the obvious gravity of the situation for the commensal bac- R. Peña-Miller ( ) · R. Beardmore Department of Mathematics, Imperial College London, London, SW7 2A7, UK e-mail: R.Pena-Miller@exeter.ac.uk Present address: R. Peña-Miller · R. Beardmore Biosciences, University of Exeter, EX4 4SB, Exeter, UK D. Lähnemann Institute of Evolution and Ecology, University of Tübingen, 72076, Tübingen, Germany H. Schulenburg Department of Evolutionary Ecology and Genetics, University of Kiel, 24118, Kiel, Germany M. Ackermann Department of Environmental Sciences, ETH Zurich, Zurich, Switzerland M. Ackermann Department of Environmental Microbiology, Eawag, Dubendorf, Switzerland