Rotating antibiotics selects optimally against antibiotic resistance, in theory

Mathematical Biosciences and Engineering

Volumn 7, Issue 3, 2010, Pages 527-552

  Beardmore, Robert E ^a   Peña Miller, Rafael ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Antibiotic rotation; Control theory; Drug resistance; Epidemiology; REB is supported by an MRC fellowship and RPM by CONACYT Mexico

Indexed keywords

ANTIINFECTIVE AGENT;

ANIMAL; ANTIBIOTIC RESISTANCE; ARTICLE; BACTERIAL INFECTION; BACTERIUM; BIOLOGICAL MODEL; DRUG ADMINISTRATION; DRUG EFFECT; GROWTH, DEVELOPMENT AND AGING; INTENSIVE CARE UNIT; MICROBIOLOGY;

ANIMALS; ANTI-BACTERIAL AGENTS; BACTERIA; BACTERIAL INFECTIONS; DRUG ADMINISTRATION SCHEDULE; DRUG RESISTANCE, BACTERIAL; INTENSIVE CARE UNITS; MODELS, BIOLOGICAL;

EID: 77954614742     PISSN: 15471063     EISSN: 15510018     Source Type: Journal    
DOI: 10.3934/mbe.2010.7.527     Document Type: Article

References (35)

1. B. Allegranzi, R. Luzzati, A. Luzzani, F. Girardini, L. Antozzi, R. Raiteri, G. Di Perri and E. Concia, Impact of antibiotic changes in empirical therapy on antimicrobial resistance in intensive care unit-acquired infections, J Hosp Infect, 52 (2002), 136-140.
2. 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.
3. S. Bonhoeffer, M. Lipsitch and B. R. Levin, Evaluating treatment protocols to prevent antibiotic resistance, PNAS, 94 (1997), 12106-12111.
4. 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.
5. T. Burden, J. Ernstberger and K. R. Fister, Optimal control applied to immunotherapy, Discrete Contin Dyn Syst Ser B, 4 (2004), 135-146.
6. E. Campbell, O. Pavlova, N. Zenkin, F. Leon, H. Irschik, R. Jansen, K. Severinov and S. Darst, Structural, functional, and genetic analysis of sorangicin inhibition of bacterial RNA polymerase, EMBO J, 24 (2005), 674-682.
7. K. C. Chow, X. Wang and C. Castillo-Chavez, A mathematical model of nosocomial infection and antibiotic resistance: Evaluating the efficacy of antimicrobial cycling programs and patient isolation on dual resistance, download from http://mtbi.asu.edu/downloads (2009).
8. E. M. C. D'Agata, M. Dupont-Rouzeyrol, P. Magal, D. Olivier and S. Ruan, The impact of different antibiotic regimens on the emergence of antimicrobial-resistant bacteria, PLoS One, 3 (2008), e4036.
9. K. Fister, S. Lenhart and J. S. McNally, Optimizing chemotherapy in an HIV model, Electron J Differential Equations, 32 (1998), 1-12.
10. W. H. Fleming and R. W. Rishel, "Deterministic and Stochastic Optimal Control," Springer- Verlag, New York, 1982.
11. R.V. Gamkrelidze, Discovery of the maximum principle, J Dynam Control Systems, 5 (1999), 437-451.
12. T. Hedrick, A. Schulman, S. McElearney, R. Smith, B. Swenson, H. Evans, J. Truwit, W. Scheld and R. Sawyer, Outbreak of resistant Pseudomonas aeruginosa infections during a quarterly cycling antibiotic regimen, Surg Infect (Larchmt), 9 (2008), 139-152.
13. P. Huovinen, Mathematical model tell us the future!, J Antimicrob Chemother, 56 (2005), 257-258.
14. R. Laxminarayan, "Bacterial Resistance and the Optimal Use of Antibiotics," Resources for the Future (2001).
15. R. Laxminarayan, "Battling Resistance to Antibiotics and Pesticides," Resources for the Future Press, 2002.
16. B. Levin and M. Bonten, Cycling antibiotics may not be good for your health, PNAS, 101 (2004), 13101-13102.
17. H. J. van Loon, M. R. Vriens, A.C. Fluit, A. Troelstra, C. van der Warken, J. Verhoef and M. Bonten, Antibiotic rotation and development of gram-negative antibiotic resistance, Am J Respir Crit Care Med, 171 (2005), 480-487.
18. J. T. Magee, The resistance ratchet: Theoretical implications of cyclic selection pressure, J Antimicrob Chemother, 56 (2005), 427-430.
19. J.A. Martinez, J.M. Nicolas, F. Marco, J.P. Horcajada, G. Garcia-Segarra, A. Trilla, C. Codina and 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.
20. R. G. Masterton, Antibiotic cycling: More than it might seem?, J Antimicrob Chemother, 55 (2005), 1-5.
21. 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.
22. G. G. Perron, A. Gonzalez and A. Buckling, Source-sink dynamics shape the evolution of antibiotic resistance and its pleiotropic fitness cost, Proc R Soc B, 274 (2007), 2351-2356.
23. D. P. Raymond, S. J. Pelletier, T. D. Crabtree, T. G. Gleason, L. L. Hamm, T. L. Pruett and R. G. Sawyer, Impact of a rotating empiric antibiotic schedule on infectious mortality in an intensive care unit, Crit Care Med, 29 (2001), 1101-1108.
24. T. C. Reluga, Simple models of antibiotic cycling, Math Med Biol, 22 (2005), 187-208.
25. R. Rowthorn and G. M. Brown, Battling resistance to antibiotics and pesticides, in "Using Antibiotics when Resistance is Renewable" (ed. R. Laxminarayan), Resources for the Future Press, (2002), 42-75.
26. A. Sandiumenge, E. Diaz, A. Rodriguez, L. Vidaur, L. Canadell, M. Olona, M. Rue and J. Rello, Impact of diversity of antibiotic use on the development of antimicrobial resistance, J Antimicrob Chemother, 57 (2006), 1197-1204.
27. Heinz Schättler, The local structure of time-optimal trajectories in dimension three under generic conditions, SIAM J Control Optim, 26 (1988), 899-918.
28. R. L. Smith, H. L. Evans, T. W. Chong, S. T. Mcelearney, T. L. Hedrick, B. R. Swenson, W. M. Scheld, T. L. Pruett and R. G. Sawyer, Reduction in rates of methicillin-resistant staphylococcus aureus infection after introduction of quarterly linezolid-vancomycin cycling in a surgical intensive care unit, Surg Infect, 9 (2008), 423-431.
29. H. J. Sussmann, A bang-bang theorem with bounds on the number of switchings, SIAM J. Control Optim, 17 (1979), 629-651.
30. H. J. Sussmann, Modern optimal control, in "Thirty Years of Optimal Control: Was the Path Unique?" (eds. E. O. Roxin), Marcel Dekker Inc., (1998), 359-375.
31. H. T. Sussmann, "The Bang-Bang Problem for Certain Control Systems in GL(n, R)," SIAM J Control, 1972.
32. P. Toltzis, M. J. Dul, C. Hoyen, A. Salvator, M. Walsh, L. Zetts and H. Toltzis, The effect of antibiotic rotation on colonization with antibiotic-resistant bacilli in a neonatal intensive care unit, Pediatrics, 110 (2002), 707-711.
33. D. K. Warren, H. A. Hill, L. R. Merz, M. H. Kollef, M. K. Hayden, V. J. Fraser and S. K. Fridkin, Cycling empirical antimicrobial agents to prevent emergence of antimicrobial-resistant gram-negative bacteria among intensive care unit patients, Crit Care Med, 32 (2004), 2450-2456.
34. M. Xu, Y. N. Zhou, B. P. Goldstein and D. J. Jin, Cross-resistance of Escherichia coli RNA polymerases conferring rifampin resistance to different antibiotics, J Bacteriol, 187 (2005), 2783-2792.
35. P. Yeh, A. I. Tschumi and R. Kishony, Functional classification of drugs by properties of their pairwise interactions, Nat Genet, 38 (2006), 489-494.