A sharp threshold for disease persistence in host metapopulations.

Thanate Dhirasakdanon, Horst R. Thieme, P. Van Den Driessche

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

A sharp threshold is established that separates disease persistence from the extinction of small disease outbreaks in an S→E→I→R→S type metapopulation model. The travel rates between patches depend on disease prevalence. The threshold is formulated in terms of a basic replacement ratio (disease reproduction number), ℛ(0), and, equivalently, in terms of the spectral bound of a transmission and travel matrix. Since frequency-dependent (standard) incidence is assumed, the threshold results do not require knowledge of a disease-free equilibrium. As a trade-off, for ℛ(0)>1, only uniform weak disease persistence is shown in general, while uniform strong persistence is proved for the special case of constant recruitment of susceptibles into the patch populations. For ℛ(0)<1, Lyapunov's direct stability method shows that small disease outbreaks do not spread much and eventually die out.

Original languageEnglish (US)
Pages (from-to)363-378
Number of pages16
JournalJournal of Biological Dynamics
Volume1
Issue number4
StatePublished - Oct 2007

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metapopulation
travel
persistence
disease prevalence
extinction
incidence
trade-off
replacement
methodology
matrix

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology

Cite this

A sharp threshold for disease persistence in host metapopulations. / Dhirasakdanon, Thanate; Thieme, Horst R.; Van Den Driessche, P.

In: Journal of Biological Dynamics, Vol. 1, No. 4, 10.2007, p. 363-378.

Research output: Contribution to journalArticle

Dhirasakdanon, T, Thieme, HR & Van Den Driessche, P 2007, 'A sharp threshold for disease persistence in host metapopulations.', Journal of Biological Dynamics, vol. 1, no. 4, pp. 363-378.
Dhirasakdanon, Thanate ; Thieme, Horst R. ; Van Den Driessche, P. / A sharp threshold for disease persistence in host metapopulations. In: Journal of Biological Dynamics. 2007 ; Vol. 1, No. 4. pp. 363-378.
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