Senescence and antibiotic resistance in an age-structured population model

Journal of Mathematical Biology

Volumn 61, Issue 4, 2010, Pages 475-499

  de Leenheer, Patrick ^a   Dockery, Jack ^b   Gedeon, Tomáš ^b   Pilyugin, Sergei S ^a  

^a UNIVERSITY OF FLORIDA   (United States)

^b MONTANA STATE UNIVERSITY   (United States)

Author keywords

Age structure; Antibiotic resistance; Asymmetric division; Coexistence; Senescence

Indexed keywords

ANTIINFECTIVE AGENT;

AGING; ANTIBIOTIC RESISTANCE; ARTICLE; BACTERIAL INFECTION; BACTERIUM; BIOLOGICAL MODEL; BIOREACTOR; DRUG EFFECT; GROWTH, DEVELOPMENT AND AGING; HUMAN; PHYSIOLOGY;

AGING; ANTI-BACTERIAL AGENTS; BACTERIA; BACTERIAL INFECTIONS; BIOREACTORS; DRUG RESISTANCE, BACTERIAL; HUMANS; MODELS, BIOLOGICAL;

EID: 77955091656     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-009-0302-7     Document Type: Article

References (46)

1. Albrich WC, Monnet DL, Harbarth S (2004) Antibiotic selection pressure and resistance in Streptococcus pneumoniae and Streptococcus pyogenes. Emerg Infect Dis 10(3): 514-517.
2. Ayati BP, Klapper I (2007) A multiscale model of biofilm as a senescence-structured fluid. SIAM Multi Model Sim 6: 347-365.
3. Balaban NQ, Merrin J, Chait R, Kowalik L, Leibler S (2005) Bacterial persistence as a phenotypic switch. Science 305: 1622-1625.
4. Bigger J (1944) Treatment of staphylococcal infections with penicillin by intermittent sterilisation. The Lancet 244: 497-500.
5. Cogan NG (2006) Effects of persister formation on bacterial response dosing. J Theor Biol 238: 694-703.
6. Cogan NG (2007) Incorporating toxin hypothesis into a mathematical model of persister formation and dynamics. J Theor Biol 248: 340-349.
7. Consortium REX (2007) Structure of the scientific community modelling the evolution of resistance. PLoS ONE 2(12): e1275. doi: 10. 1371/journal. pone. 0001275.
8. Davies J (1994) Inactivation of antibiotics and the dissemination of resistance genes. Science 264: 375-382.
9. D'Agata EMC, Magal P, Olivier D, Ruan S, Webb GF (2007) Modeling antibiotic resistance in hospitals: the impact of minimizing treatment duration. J Theor Biol 249: 487-499.
10. D'Agata EMC, Dupont-Rouzeyrol M, Magal P, Olivier D, Ruan S (2008) The impact of different antibiotic regimens on the emergence of antimicrobial-resistant bacteria. PLoS ONE 3(12): e4036. doi: 10. 1371/journal. pone. 0004036.
11. D'Agata EMC, Webb GF, Horn MA, Moellering RC Jr, Ruan S (2009) Modeling the invasion of community-acquired methicillin-resistant Staphylococcus aureusi into the hospital setting. Clin Infect Dis 48: 274-284.
12. De Leenheer P, Cogan NG (2009) Failure of antibiotic treatment in microbial populations. J Math Biol 59(4): 563-579.
13. 0 in models for infectious diseases in heterogeneous populations. J Math Biol 28: 365-382.
14. Grundmann H, Hellriegel B (2006) Mathematical modeling: a tool for hospital infection control. Lancet Infect Dis 6: 39-45.
15. Hardin G (1960) Competitive exclusion principle. Science 131: 1292-1297.
16. Hirsch MW, Hanisch H, Gabriel J-P (1985) Differential equation models for some parasitic infections: methods for the study of asymptotic behavior. Comm Pure Appl Math 38: 733-753.
17. Imran M, Smith HL (2006) The pharmacodynamics of antibiotic treatment. J Comp Math Meth Med 7: 229-263.
18. Keren I, Kaldalu N, Spoering A, Wang Y, Lewis K (2004) Persister cells and tolerance to antimicrobials. FEMS Microbiol Lett 230: 13-18.
19. Klapper I, Gilbert P, Ayati BP, Dockery J, Stewart PS (2007) Senescence can explain microbial persistence. Microbiology 153: 3623-3630.
20. Korona R, Nakatsu CH, Forney LJ, Lenski RE (1994) Evidence for multiple adaptive peaks from populations of bacteria evolving in a structured habitat. Proc Natl Acad Sci USA 91: 9037-9041.
21. Kussell E, Leibler S (2005) Phenotypic diversity, population growth, and information in fluctuating environments. Science 309: 275-278.
22. Kussell E, Kishony R, Balaban NQ, Leibler S (2005) Bacterial persistence: a model of survival in changing environments. Genetics 169: 1807-1814.
23. Layden T, Layden J, Ribeiro R, Perelson A (2003) Mathematical modeling of viral kinetics: a tool to understand and optimize therapy. Clin Liver Dis 7: 163-178.
24. Lenas P, Pavlou S (1995) Coexistence of three microbial populations in a chemostat with periodically varying dilution rate. Math Biosci 129: 111-142.
25. Levin BR (2001) Minimizing potential resistance: a population dynamics view. Clin Infect Dis 33: S161-S169.
26. Levy S, Marshall B (2004) Antibacterial resistance worldwide: causes, challenges and responses. Nat Med 10: S122-S129.
27. Lewis K (2001) Riddle of biofilm resistance. Antimicrob Agents Chemoth 45: 999-1007.
28. Lewis K (2007) Persister cells, dormancy and infectious disease. Nat Rev Micro 5: 48-56.
29. Lipsitch M, Levin B (1997) The population dynamics of antimicrobial chemotherapy. Antimicrob Agents Chemother 41: 363-373.
30. Lindner AB, Madden R, Demarez A, Stewart EJ, Taddei F (2008) Asymmetric segregation of protein aggregates is associated with cellular aging and rejuvenation. Proc Natl Acad Sci USA 105: 3076-3081.
31. Martinez JL (2008) Antibiotics and antibiotic resistance genes in natural environments. Science 321: 365-367.
32. McGowan JE (1983) Antimicrobial resistance in hospital organisms and its relation to antibiotic use. Rev Inf Dis 5(6): 1033-1048.
33. Ochman H, Lawrence JG, Groisman EA (2000) Lateral gene transfer and the nature of bacterial innovation. Nature 405: 299-304.
34. Perelson A, Nelson P (1999) Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev 41: 3-44.
35. Siegel JD, Rhinehart E, Jackson M, Chiarello L (2007) Management of multidrug-resistant organisms in health care settings, 2006. Am J Infect Control 35: S165-S193.
36. Spellberg B, Guidos R, Gilbert D, Bradley J, Boucher HW, Scheld WM, Bartlett JG, Edwards J Jr (2008) The epidemic of antibiotic-resistant infections: a call to action for the medical community from the Infectious Diseases Society of America. Clin Infect Dis 46: 155-164.
37. Smith HL, Waltman P (1995) The theory of the chemostat. Cambridge University Press, Cambridge.
38. Smith HL, Waltman P (1999) Perturbation of a globally stable steady state. Proc AMS 127: 447-453.
39. Stewart EJ, Madden R, Paul G, Taddei F (2005) Aging and death in an organism that reproduces by morphologically symmetric division. PLoS Comp Biol 3: 295-300.
40. Thieme HR (1993) Persistence under relaxed point-dissipativity (with application to an endemic model). SIAM J Math Anal 24: 407-435.
41. Thieme HR (2003) Mathematics in population biology. Princeton University Press, Princeton.
42. Temime L, Hejblum G, Setbon M, Valleron AJ (2008) The rising impact of mathematical modeling in epidemiology: antibiotic resistance research as a case study. Epidemiol Infect 136: 289-298.
43. Turner PE, Souza V, Lenski RE (1996) Tests of ecological mechanisms promoting the stable coexistence of two bacterial genotypes. Ecology 77: 2119-2129.
44. Vance RR (1985) The stable coexistence of two competitors for one resource. Am Nat 126: 72-86.
45. van den Driessche P, Watmough J (2002) Reproduction numbers and sub-treshold endemic equilibria for compartmental models of disease transmission. Math Biosci 180: 29-48.
46. Wiuff C, Anderson D (2007) Antibiotic treatment in vitro of phenotypically tolerant bacterial populations. J Antimicrob Chemother 59: 254-263.