Qualitative analysis of models with different treatment protocols to prevent antibiotic resistance

Mathematical Biosciences

Volumn 227, Issue 1, 2010, Pages 56-67

  Sun, Hong Rui ^a   Lu, Xinxin ^b   Ruan, Shigui ^c  

^a LANZHOU UNIVERSITY   (China)

^b CAPITAL MEDICAL UNIVERSITY   (China)

^c Department of Biology   (United States)

Author keywords

Antibiotic resistance; Basic reproduction number; Equilibrium; Mathematical model; Stability

Indexed keywords

CELL PROLIFERATION; CONVERGENCE OF NUMERICAL METHODS; DISEASE CONTROL; MATHEMATICAL MODELS; PHASE EQUILIBRIA;

ANTIBIOTIC RESISTANCE; BASIC REPRODUCTION NUMBER; DIFFERENT TREATMENTS; DISEASE-FREE EQUILIBRIUM; DYNAMICAL PROPERTIES; GLOBALLY ASYMPTOTICALLY STABLE; LOCAL OR GLOBAL STABILITY; QUALITATIVE ANALYSIS;

ANTIBIOTICS;

ANTIBIOTIC AGENT;

ANTIBIOTIC RESISTANCE; COMPUTER SIMULATION; NUMERICAL MODEL; QUALITATIVE ANALYSIS;

ANTIBIOTIC RESISTANCE; ANTIBIOTIC THERAPY; ARTICLE; BACTERIAL INFECTION; CLINICAL PROTOCOL; ENDEMIC DISEASE; MATHEMATICAL ANALYSIS; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; MATHEMATICAL PARAMETERS; QUALITATIVE ANALYSIS; SIMULATION;

EID: 77955276384     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2010.06.002     Document Type: Article

References (25)

1. Amarasekar P. Interference competition and species coexistence. Proc. Roy. Soc. Lond. B 2002, 269:2541.
2. Austin D.J., Anderson R.M. Studies of antibiotic resistance within the patient, hospitals and the community using simple mathematical models. Philos. Trans. Roy. Soc. Lond. B 1999, 354:721.
3. Austin D.J., Bonten M.J.M., Weinstein R.A., Slaughter S., Anderson R.M. Vancomycin-resistant enterococci in intensive-care hospital settings: transmission dynamics, persistence, and the impact of infection control programs. Proc. Natl. Acad. Sci. USA 1999, 96:6908.
4. Bergstrom C.T., Lo M., Lipsitch M. Ecological theory suggests that antimicrobial cycling will not reduce antimicrobial resistance in hospitals. Proc. Natl. Acad. Sci. USA 2004, 101:13285.
5. Boldin B., Bonten M.J., Diekmann O. Relative effects of barrier precautions and topical antibiotics on nosocomial bacterial transmission: results of multi-compartment models. Bull. Math. Biol. 2007, 69:2227.
6. Bonhoeffer S., Lipsitch M., Levin B.R. Evaluating treatment protocols to prevent antibiotic resistance. Proc. Natl. Acad. Sci. USA 1997, 94:12106.
7. Bonten M.J.M., Austin D.J., Lipsitch M. Understanding the spread of antibiotic resistant pathogens in hospitals: mathematical models as tools for control. Clin. Infect. Dis. 2001, 33:1739.
8. Brauer F., Castillo-Chavez C. Mathematical Models in Population Biology and Epidemiology 2000, Springer, New York.
9. Bremermann H.J., Thieme H.R. A competitive exclusion principle for pathogen virulence. J. Math. Biol. 1989, 27:179.
10. Busenberg S., van den Driessche P. Analysis of a disease transmission model in a population with varying size. J. Math. Biol. 1990, 28:257.
11. D'Agata E.M.C., Dupont-Rouzeyrol M., Magal P., Olivier D., Ruan S. The impact of different antibiotic regimens on the emergence of antimicrobial-resistant bacteria. PLoS ONE 2008, 3:e4036.
12. D'Agata E.M.C., Magal P., Olivier D., Ruan S., Webb G.F. Modeling antibiotic resistance in hospitals: the impact of minimizing treatment duration. J. Theor. Biol. 2007, 249:487.
13. 0 in models for infectious diseases in heterogeneous populations. J. Math. Biol. 1999, 28:365.
14. Daxboeck F., et al. Economic burden associated with multi-resistant Gram-negative organisms compared with that for methicillin-resistant Staphylococcus aureus in a university teaching hospital. J. Hosp. Infect. 2006, 62:214.
15. Grundmann H., Aires-de-Sousa M., Boyce J., Tiemersma E. Emergence and resurgence of methicillin-resistant Staphylococcus aureus as a public-health threat. Lancet 2006, 368:874.
16. Grundmann H., Hellriegel B. Mathematical modeling: a tool for hospital infection control. Lancet Infect. Dis. 2006, 6:39.
17. Klevens R.M., et al. Invasive methicillin-resistant Staphylococcus aureus infections in the United States. JAMA 2007, 298:1763.
18. Korn G.A., Korn T.M. Mathematical Handbook for Scientists and Engineers: Definitions, Theorems and Formulas for Reference and Review 2000, Dover Publications, Mineola, NY.
19. Levy S.B., Marshall B. Antibacterial resistance worldwide: causes, schallenges and responses. Nat. Med. 2004, 10:S122.
20. Reluga T.C. Simple models of antibiotic cycling. Math. Med. Biol. 2005, 22:187.
21. Spellberg B., et al. The epidemic of antibiotic-resistant infections: a call to action for the medical community from the Infectious Diseases Society of America. Clin. Infect. Dis. 2008, 46:155.
22. Smith H.L., Li B. Competition for essential resources: a brief review. Fields Institute Communications 2003, 36:213.
23. Temime L., et al. The rising impact of mathematical modeling in epidemiology: antibiotic resistance research as a case study. Epidemiol. Infect. 2008, 136:289.
24. Webb G.F., D'Agata E.M.C., Magal P., Ruan S. A model of antibiotic-resistant bacterial epidemics in hospitals. Proc. Natl. Acad. Sci. USA 2005, 102:13343.
25. Webb G.F., Horn M.A., D'Agata E.M.C., Moellering R.C., Ruan S. Competition of hospital-acquired and community-acquired methicillin-resistant Staphylococcus aureus strains in hospitals. J. Biol. Dyn. 2010, 4:115.