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 language | English (US) |
|---|---|
| Pages (from-to) | 56-67 |
| Number of pages | 12 |
| Journal | Mathematical Biosciences |
| Volume | 227 |
| Issue number | 1 |
| DOIs | |
| State | Published - Sep 1 2010 |
Keywords
- 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