A sharp threshold for disease persistence in host metapopulations

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

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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), ℛ0, 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 ℛ0>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 ℛ0<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
Issue number4
StatePublished - Oct 2007


  • Basic reproduction number
  • Extinction
  • Persistence

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology


Dive into the research topics of 'A sharp threshold for disease persistence in host metapopulations'. Together they form a unique fingerprint.

Cite this