Antibiotic cycling versus mixing: The difficulty of using mathematicalmodels to definitively quantify their relative merits

Robert E. Beardmore; Rafael Peña-Miller

doi:10.3934/mbe.2010.7.923

Article Contents

2010, Volume 7, Issue 4: 923-933. Doi: 10.3934/mbe.2010.7.923

This issue Previous Article Rotating antibiotics does not minimize selection for resistance Next Article

Antibiotic cycling versus mixing: The difficulty of using mathematical models to definitively quantify their relative merits

Robert E. Beardmore^1, and
Rafael Peña-Miller^1,

1.
Department of Mathematics, Imperial College London, SW7 2AZ, London

Received: August 31, 2010

Revised: August 31, 2010

Published: September 2010

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Abstract

We ask the question Which antibiotic deployment protocols select best against drug-resistant microbes: mixing or periodic cycling? and demonstrate that the statistical distribution of the performances of both sets of protocols, mixing and periodic cycling, must have overlapping supports. In other words, it is a general, mathematical result that there must be mixing policies that outperform cycling policies and vice versa.
As a result, we agree with the tenet of Bonhoefer et al. [1] that one should not apply the results of [2] to conclude that an antibiotic cycling policy that implements cycles of drug restriction and prioritisation on an ad-hoc basis can select against drug-resistant microbial pathogens in a clinical setting any better than random drug use. However, nor should we conclude that a random, per-patient drug-assignment protocol is the de facto optimal method for allocating antibiotics to patients in any general sense.

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Mathematics Subject Classification: 93C15, 92B05.

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