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), 919-922.

[2]

R. E. Beardmore and R. Peña-Miller, Rotating antibiotics selects optimally against antibiotic resistance, in theory, MBE, 7 (2010), 527-552. doi: doi:10.3934/mbe.2010.7.527.

[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), 13285-13290. doi: doi:10.1073/pnas.0402298101.

[4]

S. Bonhoeffer, M. Lipsitch and B. R. Levin, Evaluating treatment protocols to prevent antibiotic resistance, PNAS, 94 (1997), 12106-12111. doi: doi:10.1073/pnas.94.22.12106.

[5]

E. M. Brown and D. Nathwani, Antibiotic cycling or rotation: A systematic review of the evidence of efficacy, J. Antimicrob. Chemother., 55 (2005), 6-9. doi: doi:10.1093/jac/dkh482.

[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), 1029-1031.

[7]

T. Cohen and M. Murray, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness, Nat. Med., 10 (2004), 1117-1121. doi: doi:10.1038/nm1110.

[8]

P. Huovinen, Mathematical model tell us the future!, J. Antimicrob. Chemother., 56 (2005), 257-258. doi: doi:10.1093/jac/dki230.

[9]

J. T. Magee, The resistance ratchet: Theoretical implications of cyclic selection pressure, J. Antimicrob. Chemother., 56 (2005), 427-430. doi: doi:10.1093/jac/dki229.

[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), 329-336. doi: doi:10.1097/01.CCM.0000195010.63855.45.

[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), 1040-1048.

[12]

D. Lukkassen and P. Wall, On weak convergence of locally periodic functions, J. Nonlinear Math. Phys, 9 (2002), 47-57, arXiv:math/0210293v1.

[13]

R. G. Masterton, The new treatment paradigm and the role of carbapenems, Int. J. Antimicrob. Agents, 33 (2009), 105-110. doi: doi:10.1016/j.ijantimicag.2008.07.023.

[14]

M. G. Bergeron, Revolutionizing the practice of medicine through rapid ($<$ 1h) DNA-based diagnostics, Clin. Invest. Med., 31 (2008), E265-E271.

[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), 1269-1276. doi: doi:10.1007/s00268-005-0781-7.

[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), 28-32. doi: doi:10.1016/j.jhin.2009.11.022.

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), 919-922.

[2]

R. E. Beardmore and R. Peña-Miller, Rotating antibiotics selects optimally against antibiotic resistance, in theory, MBE, 7 (2010), 527-552. doi: doi:10.3934/mbe.2010.7.527.

[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), 13285-13290. doi: doi:10.1073/pnas.0402298101.

[4]

S. Bonhoeffer, M. Lipsitch and B. R. Levin, Evaluating treatment protocols to prevent antibiotic resistance, PNAS, 94 (1997), 12106-12111. doi: doi:10.1073/pnas.94.22.12106.

[5]

E. M. Brown and D. Nathwani, Antibiotic cycling or rotation: A systematic review of the evidence of efficacy, J. Antimicrob. Chemother., 55 (2005), 6-9. doi: doi:10.1093/jac/dkh482.

[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), 1029-1031.

[7]

T. Cohen and M. Murray, Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness, Nat. Med., 10 (2004), 1117-1121. doi: doi:10.1038/nm1110.

[8]

P. Huovinen, Mathematical model tell us the future!, J. Antimicrob. Chemother., 56 (2005), 257-258. doi: doi:10.1093/jac/dki230.

[9]

J. T. Magee, The resistance ratchet: Theoretical implications of cyclic selection pressure, J. Antimicrob. Chemother., 56 (2005), 427-430. doi: doi:10.1093/jac/dki229.

[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), 329-336. doi: doi:10.1097/01.CCM.0000195010.63855.45.

[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), 1040-1048.

[12]

D. Lukkassen and P. Wall, On weak convergence of locally periodic functions, J. Nonlinear Math. Phys, 9 (2002), 47-57, arXiv:math/0210293v1.

[13]

R. G. Masterton, The new treatment paradigm and the role of carbapenems, Int. J. Antimicrob. Agents, 33 (2009), 105-110. doi: doi:10.1016/j.ijantimicag.2008.07.023.

[14]

M. G. Bergeron, Revolutionizing the practice of medicine through rapid ($<$ 1h) DNA-based diagnostics, Clin. Invest. Med., 31 (2008), E265-E271.

[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), 1269-1276. doi: doi:10.1007/s00268-005-0781-7.

[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), 28-32. doi: doi:10.1016/j.jhin.2009.11.022.

[1]

Robert E. Beardmore, Rafael Peña-Miller. Rotating antibiotics selects optimally against antibiotic resistance, in theory. Mathematical Biosciences & Engineering, 2010, 7 (3) : 527-552. doi: 10.3934/mbe.2010.7.527
[2]

Michele L. Joyner, Cammey C. Manning, Whitney Forbes, Michelle Maiden, Ariel N. Nikas. A physiologically-based pharmacokinetic model for the antibiotic ertapenem. Mathematical Biosciences & Engineering, 2016, 13 (1) : 119-133. doi: 10.3934/mbe.2016.13.119
[3]

Mudassar Imran, Hal L. Smith. A model of optimal dosing of antibiotic treatment in biofilm. Mathematical Biosciences & Engineering, 2014, 11 (3) : 547-571. doi: 10.3934/mbe.2014.11.547
[4]

Mudassar Imran, Hal L. Smith. The dynamics of bacterial infection, innate immune response, and antibiotic treatment. Discrete and Continuous Dynamical Systems - B, 2007, 8 (1) : 127-143. doi: 10.3934/dcdsb.2007.8.127
[5]

Michele L. Joyner, Cammey C. Manning, Brandi N. Canter. Modeling the effects of introducing a new antibiotic in a hospital setting: A case study. Mathematical Biosciences & Engineering, 2012, 9 (3) : 601-625. doi: 10.3934/mbe.2012.9.601
[6]

Kaifa Wang, Aijun Fan. Uniform persistence and periodic solution of chemostat-type model with antibiotic. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 789-795. doi: 10.3934/dcdsb.2004.4.789
[7]

Colette Calmelet, John Hotchkiss, Philip Crooke. A mathematical model for antibiotic control of bacteria in peritoneal dialysis associated peritonitis. Mathematical Biosciences & Engineering, 2014, 11 (6) : 1449-1464. doi: 10.3934/mbe.2014.11.1449
[8]

Urszula Ledzewicz, Heinz Schättler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete and Continuous Dynamical Systems - B, 2006, 6 (1) : 129-150. doi: 10.3934/dcdsb.2006.6.129
[9]

Cristian Tomasetti, Doron Levy. An elementary approach to modeling drug resistance in cancer. Mathematical Biosciences & Engineering, 2010, 7 (4) : 905-918. doi: 10.3934/mbe.2010.7.905
[10]

Avner Friedman, Najat Ziyadi, Khalid Boushaba. A model of drug resistance with infection by health care workers. Mathematical Biosciences & Engineering, 2010, 7 (4) : 779-792. doi: 10.3934/mbe.2010.7.779
[11]

Zhenzhen Chen, Sze-Bi Hsu, Ya-Tang Yang. The continuous morbidostat: A chemostat with controlled drug application to select for drug resistance mutants. Communications on Pure and Applied Analysis, 2020, 19 (1) : 203-220. doi: 10.3934/cpaa.2020011
[12]

Nicolas Bacaër, Cheikh Sokhna. A reaction-diffusion system modeling the spread of resistance to an antimalarial drug. Mathematical Biosciences & Engineering, 2005, 2 (2) : 227-238. doi: 10.3934/mbe.2005.2.227
[13]

Urszula Ledzewicz, Shuo Wang, Heinz Schättler, Nicolas André, Marie Amélie Heng, Eddy Pasquier. On drug resistance and metronomic chemotherapy: A mathematical modeling and optimal control approach. Mathematical Biosciences & Engineering, 2017, 14 (1) : 217-235. doi: 10.3934/mbe.2017014
[14]

Ami B. Shah, Katarzyna A. Rejniak, Jana L. Gevertz. Limiting the development of anti-cancer drug resistance in a spatial model of micrometastases. Mathematical Biosciences & Engineering, 2016, 13 (6) : 1185-1206. doi: 10.3934/mbe.2016038
[15]

Qi Deng, Zhipeng Qiu, Ting Guo, Libin Rong. Modeling within-host viral dynamics: The role of CTL immune responses in the evolution of drug resistance. Discrete and Continuous Dynamical Systems - B, 2021, 26 (7) : 3543-3562. doi: 10.3934/dcdsb.2020245
[16]

Timothy C. Reluga, Jan Medlock, Alison Galvani. The discounted reproductive number for epidemiology. Mathematical Biosciences & Engineering, 2009, 6 (2) : 377-393. doi: 10.3934/mbe.2009.6.377
[17]

Jacques Demongeot, Mohamad Ghassani, Mustapha Rachdi, Idir Ouassou, Carla Taramasco. Archimedean copula and contagion modeling in epidemiology. Networks and Heterogeneous Media, 2013, 8 (1) : 149-170. doi: 10.3934/nhm.2013.8.149
[18]

Carlos M. Hernández-Suárez, Oliver Mendoza-Cano. Applications of occupancy urn models to epidemiology. Mathematical Biosciences & Engineering, 2009, 6 (3) : 509-520. doi: 10.3934/mbe.2009.6.509
[19]

Luca Gerardo-Giorda, Pierre Magal, Shigui Ruan, Ousmane Seydi, Glenn Webb. Preface: Population dynamics in epidemiology and ecology. Discrete and Continuous Dynamical Systems - B, 2020, 25 (6) : i-ii. doi: 10.3934/dcdsb.2020125
[20]

Krzysztof Frączek, Leonid Polterovich. Growth and mixing. Journal of Modern Dynamics, 2008, 2 (2) : 315-338. doi: 10.3934/jmd.2008.2.315

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (36)
  • HTML views (0)
  • Cited by (20)

Other articles
by authors

[Back to Top]

Copyright © 2022 American Institute of Mathematical Sciences | Privacy Policy