Infinite subharmonic bifurcation in an SEIR epidemic model

Ira B. Schwartz, Hal Smith

Research output: Contribution to journalArticlepeer-review

194 Scopus citations


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
Issue number3
StatePublished - Dec 1 1983


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

ASJC Scopus subject areas

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


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