Skip to main content
SpringerLink
Log in

Multiple stable subharmonics for a periodic epidemic model

  • Published:
Journal of Mathematical Biology Aims and scope Submit manuscript

Abstract

The S → I → R epidemic model of K. Dietz with annual oscillation in the contact rate is shown to have multiple stable subharmonic solutions of different integral year periods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anderson, R. M., May, R. M.: Directly transmitted infectious diseases. Control by vaccination. Science 215, 1053–1060 (1982)

    Google Scholar 

  2. Chow, S. N., Hale, J. K., Mallet-Paret, J.: An example of bifurcation to homoclinic orbits. J. D. E. 37, 351–373 (1980)

    Google Scholar 

  3. Dietz, K.: The incidence of infectious diseases under the influence of seasonal fluctuations. Lecture notes in biomath., vol. 11, pp. 1–5. Berlin-Heidelberg-New York: Springer 1976

    Google Scholar 

  4. Grossman, Z., Gumowski, I., Dietz, K.: The incidence of infectious diseases under the influence of seasonal fluctuations — analytic approach. In: Nonlinear systems and applications to life sciences, pp. 525–546. New York: Academic Press 1977

    Google Scholar 

  5. Grossman, Z.: Oscillatory phenomena in a model of infectious diseases. Theoret. Population Biology 18, 204–243 (1980)

    Google Scholar 

  6. Hale, J., Taboas, P.: Interaction of damping and forcing in a second order equation. Nonlinear Analysis T.M.A. 2, 77–84 (1978)

    Google Scholar 

  7. Hethcote, H.: Qualitative analyses of communicable disease models. Math. Biosciences 28, 335–356 (1976)

    Google Scholar 

  8. Hoppensteadt, F., Flaherty, J.: Frequency entrainment of a forced Van der Pol oscillator. Studies in Applied Math. 58, 5–15 (1978)

    Google Scholar 

  9. London, W. P., Yorke, J. A.: Recurrent outbreaks of measles, chickenpox and mumps. I. Seasonal variation in contact rates. Amer. J. Epidemiol. 98, 453–468 (1973)

    Google Scholar 

  10. Smith, H. L.: Subharmonic bifurcation in an S-I-R epidemic model. J. Math. Biol. 17, 163–177 (1983)

    Google Scholar 

  11. Soper, H. E.: The interpretation of periodicity in disease prevalence. J. Royal Statist. Soc. 92, 34–73 (1929)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Arizona State University, 85287, Tempe, AZ, USA

    H. L. Smith

Authors
  1. H. L. Smith
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Smith, H.L. Multiple stable subharmonics for a periodic epidemic model. J. Math. Biology 17, 179–190 (1983). https://doi.org/10.1007/BF00305758

Download citation

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00305758

Key words

Search

Navigation