Subharmonic bifurcation in an S-I-R epidemic model

Hal Smith

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


An S → I → R epidemic model with annual oscillation in the contact rate is analyzed for the existence of subharmonic solutions of period two years. We prove that a stable period two solution bifurcates from a period one solution as the amplitude of oscillation in the contact rate exceeds a threshold value. This makes rigorous earlier formal arguments of Z. Grossman, I. Gumowski, and K. Dietz [4].

Original languageEnglish (US)
Pages (from-to)163-177
Number of pages15
JournalJournal Of Mathematical Biology
Issue number2
StatePublished - Jun 1 1983


  • Bifurcation
  • Epidemic model
  • Subharmonic solution

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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