Subharmonic bifurcation in an S-I-R epidemic model

Research output: Contribution to journalArticle

55 Citations (Scopus)

Abstract

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
Volume17
Issue number2
DOIs
StatePublished - Jun 1983

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Si
Subharmonics
Epidemic Model
oscillation
Bifurcation
Period Two Solutions
Contact
Oscillation
Subharmonic Solutions
Threshold Value
Contacts (fluid mechanics)
Annual
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Keywords

  • Bifurcation
  • Epidemic model
  • Subharmonic solution

ASJC Scopus subject areas

  • Mathematics (miscellaneous)
  • Agricultural and Biological Sciences (miscellaneous)

Cite this

Subharmonic bifurcation in an S-I-R epidemic model. / Smith, Hal.

In: Journal of Mathematical Biology, Vol. 17, No. 2, 06.1983, p. 163-177.

Research output: Contribution to journalArticle

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