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

Hong Rui Sun, Xinxin Lu, Shigui Ruan

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

This paper is concerned with the qualitative analysis of two models [S. Bonhoeffer, M. Lipsitch, B.R. Levin, Evaluating treatment protocols to prevent antibiotic resistance, Proc. Natl. Acad. Sci. USA 94 (1997) 12106] for different treatment protocols to prevent antibiotic resistance. Detailed qualitative analysis about the local or global stability of the equilibria of both models is carried out in term of the basic reproduction number R0. For the model with a single antibiotic therapy, we show that if R0<1, then the disease-free equilibrium is globally asymptotically stable; if R0>1, then the disease-endemic equilibrium is globally asymptotically stable. For the model with multiple antibiotic therapies, stabilities of various equilibria are analyzed and combining treatment is shown better than cycling treatment. Numerical simulations are performed to show that the dynamical properties depend intimately upon the parameters.

Original languageEnglish (US)
Pages (from-to)56-67
Number of pages12
JournalMathematical Biosciences
Volume227
Issue number1
DOIs
StatePublished - Sep 2010

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Keywords

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

ASJC Scopus subject areas

  • Medicine(all)
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Modeling and Simulation
  • Statistics and Probability
  • Applied Mathematics

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