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

Hong Rui Sun, Xinxin Lu, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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
Issue number1
StatePublished - Sep 2010


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

ASJC Scopus subject areas

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


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