Journal of Mathematical Biology

, Volume 18, Issue 3, pp 233–253

Infinite subharmonic bifurcation in an SEIR epidemic model

  • Ira B. Schwartz
  • H. L. Smith

DOI: 10.1007/BF00276090

Cite this article as:
Schwartz, I.B. & Smith, H.L. J. Math. Biology (1983) 18: 233. doi:10.1007/BF00276090


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.

Key words

Epidemic modellingMeaslesSubharmonic bifurcationInfectious diseasesChaosMathematical modelling

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Ira B. Schwartz
    • 1
  • H. L. Smith
    • 2
  1. 1.Laboratory of Mathematical Biology, Building 10, Room 4B56National Institutes of HealthBethesdaUSA
  2. 2.Department of MathematicsArizona State UniversityTempeUSA
  3. 3.U.S. Naval Research LaboratoryWashington DCUSA