Backward bifurcation in a discrete SIS model with vaccination

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A simple discrete SIS model with vaccination is proposed. Its dynamics depend on a lumped parameter Rvac. The model exhibits the classical threshold behavior when vaccination is totally ineffective. When vaccination is partially effective, a backward transcritical bifurcation may occur at R vac = 1. In this case, the model also undergoes a saddle-node bifurcation at certain parameter values when Rvac < 1. The disease can persist for Rvac > 1 and can be eradicated for R vac < 1 if a forward transcritical bifurcation occurs at R vac = 1. However, the disease may persist even when Rvac < 1 if a backward bifurcation occurs at Rvac = 1.

Original languageEnglish
Pages (from-to)479-494
Number of pages16
JournalJournal of Biological Systems
Issue number4
StatePublished - Dec 2008


  • Saddle-node bifurcation
  • Transcritical bifurcation
  • Uniform persistence


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