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Bulletin of Mathematical Biology

, Volume 74, Issue 4, pp 908–934 | Cite as

Selecting Against Antibiotic-Resistant Pathogens: Optimal Treatments in the Presence of Commensal Bacteria

  • Rafael Peña-Miller
  • David Lähnemann
  • Hinrich Schulenburg
  • Martin Ackermann
  • Robert Beardmore
Original Article

Abstract

Using optimal control theory as the basic theoretical tool, we investigate the efficacy of different antibiotic treatment protocols in the most exacting of circumstances, 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 bacterial 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 bacteriostatic 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 bacterium, we show by example that it is possible to design drug deployment protocols that support the commensal and reduce the pathogen load. This may be achieved by appropriately fluctuating the concentration of drug in the environment; a result that is to be anticipated from the theory optimal control where bang-bang solutions may be interpreted as intermittent periods of either maximal and minimal drug deployment. While such ‘antibiotic pulsing’ is near-optimal for a wide range of treatment objectives, we also use this model to evaluate the efficacy of different antibiotic usage strategies to show that dynamically changing antimicrobial therapies may be effective in clearing a bacterial infection even when every ‘static monotherapy’ fails.

Keywords

Evolution of antimicrobial resistance Control theory 

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Copyright information

© Society for Mathematical Biology 2011

Authors and Affiliations

  • Rafael Peña-Miller
    • 1
    • 2
  • David Lähnemann
    • 3
  • Hinrich Schulenburg
    • 4
  • Martin Ackermann
    • 5
    • 6
  • Robert Beardmore
    • 1
    • 2
  1. 1.Department of MathematicsImperial College LondonLondonUK
  2. 2.BiosciencesUniversity of ExeterExeterUK
  3. 3.Institute of Evolution and EcologyUniversity of TübingenTübingenGermany
  4. 4.Department of Evolutionary Ecology and GeneticsUniversity of KielKielGermany
  5. 5.Department of Environmental SciencesETH ZurichZurichSwitzerland
  6. 6.Department of Environmental MicrobiologyEawagDubendorfSwitzerland

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