Oscillations in a patchy environment disease model

Fred Brauer, P. van den Driessche, Lin Wang

Research output: Contribution to journalArticle

16 Citations (Scopus)

Abstract

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
Volume215
Issue number1
DOIs
StatePublished - Sep 1 2008
Externally publishedYes

Fingerprint

disease models
travel
Patch
oscillation
Oscillation
Hopf bifurcation
bifurcation
Basic Reproduction Number
Switches
death
immunity
angle of incidence
Basic Reproduction number
Model
Endemic Equilibrium
Globally Asymptotically Stable
Delay-dependent
Characteristic equation
Immunity
Local Stability

Keywords

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

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Oscillations in a patchy environment disease model. / Brauer, Fred; van den Driessche, P.; Wang, Lin.

In: Mathematical Biosciences, Vol. 215, No. 1, 01.09.2008, p. 1-10.

Research output: Contribution to journalArticle

Brauer, Fred ; van den Driessche, P. ; Wang, Lin. / Oscillations in a patchy environment disease model. In: Mathematical Biosciences. 2008 ; Vol. 215, No. 1. pp. 1-10.
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