Mathematical Biosciences and Engineering (MBE)

Rotating antibiotics selects optimally against antibiotic resistance, in theory

Pages: 527 - 552, Volume 7, Issue 3, July 2010      doi:10.3934/mbe.2010.7.527

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Robert E. Beardmore - Department of Mathematics, Imperial College London, SW7 2AZ, London, United Kingdom (email)
Rafael Peña-Miller - Department of Mathematics, Imperial College London, SW7 2AZ, London, United Kingdom (email)

Abstract: The purpose of this paper is to use mathematical models to investigate the claim made in the medical literature over a decade ago that the routine rotation of antibiotics in an intensive care unit (ICU) will select against the evolution and spread of antibiotic-resistant pathogens. In contrast, previous theoretical studies addressing this question have demonstrated that routinely changing the drug of choice for a given pathogenic infection may in fact lead to a greater incidence of drug resistance in comparison to the random deployment of different drugs.
   Using mathematical models that do not explicitly incorporate the spatial dynamics of pathogen transmission within the ICU or hospital and assuming the antibiotics are from distinct functional groups, we use a control theoretic-approach to prove that one can relax the medical notion of what constitutes an antibiotic rotation and so obtain protocols that are arbitrarily close to the optimum. Finally, we show that theoretical feedback control measures that rotate between different antibiotics motivated directly by the outcome of clinical studies can be deployed to good effect to reduce the prevalence of antibiotic resistance below what can be achieved with random antibiotic use.

Keywords:  Control theory, epidemiology, antibiotic rotation, drug resistance.
Mathematics Subject Classification:  93C15, 92B05.

Received: September 2009;      Accepted: March 2010;      Available Online: June 2010.