Infinite subharmonic bifurcation in an SEIR epidemic model

Ira B. Schwartz, Hal Smith

Research output: Contribution to journalArticle

150 Citations (Scopus)

Abstract

The existence of both periodic and aperiodic behavior in recurrent epidemics is now well-documented. In this paper, it is proven that for epidemic models that incur permanent immunity with seasonal variations in the contact rate, there exists an infinite number of stable subharmonic solutions. Random effects in the environment could perturb the state of the dynamics from the domain of attraction from one subharmonic to another, thus producing aperiodic levels of incidence.

Original languageEnglish (US)
Pages (from-to)233-253
Number of pages21
JournalJournal of Mathematical Biology
Volume18
Issue number3
DOIs
StatePublished - Dec 1983

Fingerprint

Subharmonic Solutions
Subharmonics
Domain of Attraction
Epidemic Model
Immunity
Random Effects
Incidence
Bifurcation
Contact
angle of incidence
immunity
seasonal variation

Keywords

  • Chaos
  • Epidemic modelling
  • Infectious diseases
  • Mathematical modelling
  • Measles
  • Subharmonic bifurcation

ASJC Scopus subject areas

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

Cite this

Infinite subharmonic bifurcation in an SEIR epidemic model. / Schwartz, Ira B.; Smith, Hal.

In: Journal of Mathematical Biology, Vol. 18, No. 3, 12.1983, p. 233-253.

Research output: Contribution to journalArticle

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