Oscillations in a patchy environment disease model

Fred Brauer, P. van den Driessche, Lin Wang

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


For a single patch SIRS model with a period of immunity of fixed length, recruitment-death demographics, disease related deaths and mass action incidence, the basic reproduction number R0 is identified. It is shown that the disease-free equilibrium is globally asymptotically stable if R0 < 1. For R0 > 1, local stability of the endemic equilibrium and Hopf bifurcation analysis about this equilibrium are carried out. Moreover, a practical numerical approach to locate the bifurcation values for a characteristic equation with delay-dependent coefficients is provided. For a two patch SIRS model with travel, it is shown that there are several threshold quantities determining its dynamic behavior and that travel can reduce oscillations in both patches; travel may enhance oscillations in both patches; or travel can switch oscillations from one patch to another.

Original languageEnglish (US)
Pages (from-to)1-10
Number of pages10
JournalMathematical Biosciences
Issue number1
StatePublished - Sep 2008
Externally publishedYes


  • Basic reproduction number
  • Delay
  • Global asymptotic stability
  • Hopf bifurcation
  • Oscillation
  • Travel between patches

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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