Backward bifurcations in simple vaccination/treatment models

Fred Brauer

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


We describe and analyse by elementary means some simple models for disease transmission with vaccination and treatment. In particular, we give conditions for the existence of multiple endemic equilibria and backward bifurcations. The results are applicable to epidemic models in which demographic effects are ignored, but there is temporary immunity following recovery from infection.

Original languageEnglish (US)
Pages (from-to)410-418
Number of pages9
JournalJournal of biological dynamics
Issue number5
StatePublished - Sep 2011


  • Backward bifurcation
  • Temporary immunity
  • Treatment
  • Vaccination

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Ecology


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