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Mathematical Biosciences and Engineering (MBE)
 

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

Pages: 923 - 933, Volume 7, Issue 4, October 2010      doi:10.3934/mbe.2010.7.923

 
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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: 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.

Keywords:  Epidemiology, antibiotic cycling, antibiotic mixing, drug resistance.
Mathematics Subject Classification:  93C15, 92B05.

Received: September 2010;      Accepted: September 2010;      Published: October 2010.

 References