American Institute of Mathematical Sciences

Advanced
2010, 7(4): 923-933. doi: 10.3934/mbe.2010.7.923

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, United Kingdom

Received  September 2010 Revised  September 2010 Published  October 2010

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: antibiotic mixing, Epidemiology, drug resistance., antibiotic cycling.
Mathematics Subject Classification: 93C15, 92B0.
Citation: Robert E. Beardmore, Rafael Peña-Miller. Antibiotic cycling versus mixing: The difficulty of using mathematical models to definitively quantify their relative merits. Mathematical Biosciences & Engineering, 2010, 7 (4) : 923-933. doi: 10.3934/mbe.2010.7.923
References:
[1]

S. Bonhoeffer, P. S. Zur Wiesch and R. D. Kouyos, Rotating antibiotics does not minimize selection for resistance,, MBE, 7 (2010), 919.   Google Scholar

[2]

R. E. Beardmore and R. Peña-Miller, Rotating antibiotics selects optimally against antibiotic resistance, in theory,, MBE, 7 (2010), 527.  doi: doi:10.3934/mbe.2010.7.527.  Google Scholar

[3]

C. T. Bergstrom, M. Lo and M. Lipsitch, Ecological theory suggests that antimicrobial cycling will not reduce antimicrobial resistance in hospitals,, PNAS, 101 (2004), 13285.  doi: doi:10.1073/pnas.0402298101.  Google Scholar

[4]

S. Bonhoeffer, M. Lipsitch and B. R. Levin, Evaluating treatment protocols to prevent antibiotic resistance,, PNAS, 94 (1997), 12106.  doi: doi:10.1073/pnas.94.22.12106.  Google Scholar

[5]

E. M. Brown and D. Nathwani, Antibiotic cycling or rotation: A systematic review of the evidence of efficacy,, J. Antimicrob. Chemother., 55 (2005), 6.  doi: doi:10.1093/jac/dkh482.  Google Scholar

[6]

M. Niederman, Is 'crop rotation' of antibiotics the solution to a 'resistant' problem in the ICU?,, Am. J. Respir. Crit. Care Med., 156 (1997), 1029.   Google Scholar

[7]

T. Cohen and M. Murray, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness,, Nat. Med., 10 (2004), 1117.  doi: doi:10.1038/nm1110.  Google Scholar

[8]

P. Huovinen, Mathematical model tell us the future!,, J. Antimicrob. Chemother., 56 (2005), 257.  doi: doi:10.1093/jac/dki230.  Google Scholar

[9]

J. T. Magee, The resistance ratchet: Theoretical implications of cyclic selection pressure,, J. Antimicrob. Chemother., 56 (2005), 427.  doi: doi:10.1093/jac/dki229.  Google Scholar

[10]

J. A. Martinez, J. M. Nicolas, F. Marco, J. P. Horcajada, G. Garcia-Segarra, A. Trilla, C. Codina, A. Torres and J. Mensa, Comparison of antimicrobial cycling and mixing strategies in two medical intensive care units,, Crit. Care Med., 34 (2006), 329.  doi: doi:10.1097/01.CCM.0000195010.63855.45.  Google Scholar

[11]

M. H. Kollef, J. Vlasnik, L. Sharpless, C. Pasque, D. Murphy and V. Fraser, Scheduled change of antibiotic classes: A strategy to decrease the incidence of ventilator-associated pneumonia,, Am. J. Respir. Crit. Care Med., 156 (1997), 1040.   Google Scholar

[12]

D. Lukkassen and P. Wall, On weak convergence of locally periodic functions,, J. Nonlinear Math. Phys, 9 (2002), 47.   Google Scholar

[13]

R. G. Masterton, The new treatment paradigm and the role of carbapenems,, Int. J. Antimicrob. Agents, 33 (2009), 105.  doi: doi:10.1016/j.ijantimicag.2008.07.023.  Google Scholar

[14]

M. G. Bergeron, Revolutionizing the practice of medicine through rapid ($<$ 1h) DNA-based diagnostics,, Clin. Invest. Med., 31 (2008).   Google Scholar

[15]

Y. Takesue, H. Ohge, M. Sakashita, T. Sudo, Y. Murakami, K. Uemura and T. Sueda, Effect of antibiotic heterogeneity on the development of infections with antibiotic-resistant gram-negative organisms in a non-intensive care unit surgical ward,, World J. Surg., 30 (2006), 1269.  doi: doi:10.1007/s00268-005-0781-7.  Google Scholar

[16]

Y. Takesue, K. Nakajima, K. Ichiki, M. Ishihara, Y. Wada, Y. Takahashi, T. Tsuchida, T and H. Ikeuchi, Impact of a hospital-wide programme of heterogeneous antibiotic use on the development of antibiotic-resistant Gram-negative bacteria,, J. Hosp. Infect., 75 (2010), 28.  doi: doi:10.1016/j.jhin.2009.11.022.  Google Scholar

show all references

References:
[1]

S. Bonhoeffer, P. S. Zur Wiesch and R. D. Kouyos, Rotating antibiotics does not minimize selection for resistance,, MBE, 7 (2010), 919.   Google Scholar

[2]

R. E. Beardmore and R. Peña-Miller, Rotating antibiotics selects optimally against antibiotic resistance, in theory,, MBE, 7 (2010), 527.  doi: doi:10.3934/mbe.2010.7.527.  Google Scholar

[3]

C. T. Bergstrom, M. Lo and M. Lipsitch, Ecological theory suggests that antimicrobial cycling will not reduce antimicrobial resistance in hospitals,, PNAS, 101 (2004), 13285.  doi: doi:10.1073/pnas.0402298101.  Google Scholar

[4]

S. Bonhoeffer, M. Lipsitch and B. R. Levin, Evaluating treatment protocols to prevent antibiotic resistance,, PNAS, 94 (1997), 12106.  doi: doi:10.1073/pnas.94.22.12106.  Google Scholar

[5]

E. M. Brown and D. Nathwani, Antibiotic cycling or rotation: A systematic review of the evidence of efficacy,, J. Antimicrob. Chemother., 55 (2005), 6.  doi: doi:10.1093/jac/dkh482.  Google Scholar

[6]

M. Niederman, Is 'crop rotation' of antibiotics the solution to a 'resistant' problem in the ICU?,, Am. J. Respir. Crit. Care Med., 156 (1997), 1029.   Google Scholar

[7]

T. Cohen and M. Murray, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness,, Nat. Med., 10 (2004), 1117.  doi: doi:10.1038/nm1110.  Google Scholar

[8]

P. Huovinen, Mathematical model tell us the future!,, J. Antimicrob. Chemother., 56 (2005), 257.  doi: doi:10.1093/jac/dki230.  Google Scholar

[9]

J. T. Magee, The resistance ratchet: Theoretical implications of cyclic selection pressure,, J. Antimicrob. Chemother., 56 (2005), 427.  doi: doi:10.1093/jac/dki229.  Google Scholar

[10]

J. A. Martinez, J. M. Nicolas, F. Marco, J. P. Horcajada, G. Garcia-Segarra, A. Trilla, C. Codina, A. Torres and J. Mensa, Comparison of antimicrobial cycling and mixing strategies in two medical intensive care units,, Crit. Care Med., 34 (2006), 329.  doi: doi:10.1097/01.CCM.0000195010.63855.45.  Google Scholar

[11]

M. H. Kollef, J. Vlasnik, L. Sharpless, C. Pasque, D. Murphy and V. Fraser, Scheduled change of antibiotic classes: A strategy to decrease the incidence of ventilator-associated pneumonia,, Am. J. Respir. Crit. Care Med., 156 (1997), 1040.   Google Scholar

[12]

D. Lukkassen and P. Wall, On weak convergence of locally periodic functions,, J. Nonlinear Math. Phys, 9 (2002), 47.   Google Scholar

[13]

R. G. Masterton, The new treatment paradigm and the role of carbapenems,, Int. J. Antimicrob. Agents, 33 (2009), 105.  doi: doi:10.1016/j.ijantimicag.2008.07.023.  Google Scholar

[14]

M. G. Bergeron, Revolutionizing the practice of medicine through rapid ($<$ 1h) DNA-based diagnostics,, Clin. Invest. Med., 31 (2008).   Google Scholar

[15]

Y. Takesue, H. Ohge, M. Sakashita, T. Sudo, Y. Murakami, K. Uemura and T. Sueda, Effect of antibiotic heterogeneity on the development of infections with antibiotic-resistant gram-negative organisms in a non-intensive care unit surgical ward,, World J. Surg., 30 (2006), 1269.  doi: doi:10.1007/s00268-005-0781-7.  Google Scholar

[16]

Y. Takesue, K. Nakajima, K. Ichiki, M. Ishihara, Y. Wada, Y. Takahashi, T. Tsuchida, T and H. Ikeuchi, Impact of a hospital-wide programme of heterogeneous antibiotic use on the development of antibiotic-resistant Gram-negative bacteria,, J. Hosp. Infect., 75 (2010), 28.  doi: doi:10.1016/j.jhin.2009.11.022.  Google Scholar

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