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Mathematical Medicine and Biology Advance Access originally published online on March 18, 2005
Mathematical Medicine and Biology 2005 22(2):187-208; doi:10.1093/imammb/dqi002
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© The author 2005. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

Articles

Simple models of antibiotic cycling

Timothy C. Reluga**

Department of Applied Mathematics, University of Washington, Box 352420 Seattle, WA 98195-2420, USA

** Email: treluga{at}amath.washington.edu

The use of environmental heterogeneity is an old but potentially powerful method for managing biological systems. Determining the optimal form of environmental heterogeneity is a difficult problem. One family of heterogeneous management strategies that has received attention in the medical community is the periodic cycling of antibiotic usage to control antibiotic resistance. This paper presents a theory for the optimization of antibiotic cycling based on a density-independent model of transmission and immigration of evolutionarily static strains. In the case of two pathogen strains, I show that the population's asymptotic growth rate is a monotonically increasing function of the oscillation period under certain common assumptions. Monte Carlo simulations show that this result fails in more general settings, but suggest that antibiotic cycling seldom provides a significant improvement over alternative mixing practices. The results support the findings of other researchers that antibiotic cycling does not offer significant advantages over idealized conventional practice. However, cycling strategies may be preferable in some special cases.

Keywords: heterogeneous environments; resistance management

Received on 28 May 2004. accepted on 8 November 2004.


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