Skip to main content
SpringerLink
Log in
Book cover

Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases pp 207–220Cite as

Age of Infection Epidemic Models

  • Chapter
  • First Online:

Abstract

The age of infection model, first introduced by Kermack and McKendrick in 1927, is a general structure for compartmental epidemic models, including models with heterogeneous mixing. It is possible to estimate the basic reproduction number if the initial exponential growth rate and the infectivity as a function of time since being infected are known, and this is also possible for models with heterogeneous mixing.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Blythe, S.P., Busenberg, S., Castillo-Chavez, C.: Affinity and paired-event probability. Math. Biosci. 128, 265–284 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  2. Blythe, S.P., Castillo-Chavez, C., Palmer, J., Cheng, M.: Towards a unified theory of mixing and pair formation. Math. Biosci. 107, 379–405 (1991)

    Article  MATH  Google Scholar 

  3. Brauer, F.: Epidemic models with heterogeneous mixing and treatment. Bull. Math. Biol. 70, 1869–1885 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  4. Brauer, F., Watmough, J.: Age of infection epidemic models with heterogeneous mixing. J. Biol. Dyn. 3, 324–330 (2009)

    Article  MathSciNet  Google Scholar 

  5. Busenberg, S., Castillo-Chavez, C.: Interaction, pair formation and force of infection terms in sexually transmitted diseases. In: Castillo-Chavez, C. (ed.) Mathematical and Statistical Approaches to AIDS Epidemiology. Lecture Notes in Biomathematics, vol. 83, pp. 289–300. Springer, Berlin (1989)

    Chapter  Google Scholar 

  6. Diekmann, O., Heesterbeek, J.A.P., Metz, J.A.J.: The legacy of Kermack and McKendrick. In: Mollison, D. (ed.) Epidemic Models: Their Structure and Relation to Data, pp. 95–115. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  7. Kermack, W.O., McKendrick, A.G.: A contribution to the mathematical theory of epidemics. Proc. R. Soc. Lond. 115, 700–721 (1927)

    Article  MATH  Google Scholar 

  8. Kermack, W.O., McKendrick, A.G.: Contributions to the mathematical theory of epidemics, part. II. Proc. R. Soc. Lond. 138, 55–83 (1932)

    Article  MATH  Google Scholar 

  9. Kermack, W.O., McKendrick, A.G.: Contributions to the mathematical theory of epidemics, part. III. Proc. R. Soc. Lond. 141, 94–112 (1933)

    Article  MATH  Google Scholar 

  10. Nold, A.: Heterogeneity in disease transmission modeling. Math. Biosci. 52, 227–240 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  11. Thieme, H.R., Castillo-Chavez, C.: On the role of variable infectivity in the dynamics of the human immunodeficiency virus. In: Castillo-Chavez, C. (ed.) Mathematical and Statistical Approaches to AIDS Epidemiology. Lecture Notes in Biomathematics, pp. 200–217. Springer, Berlin (1989)

    Google Scholar 

  12. Thieme, H.R., Castillo-Chavez, C.: How may infection-age dependent infectivity affect the dynamics of HIV/AIDS? SIAM J. Appl. Math. 53, 1447–1479 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  13. van den Driessche, P., Watmough, J.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  14. Wallinga, J., Lipsitch, M.: How generation intervals shape the relationship between growth rates and reproductive numbers. Proc. R. Soc. B 274, 599–604 (2007)

    Article  Google Scholar 

Download references

Acknowledgments

This work was supported by the Natural Sciences and Engineering Research Council of Canada.

Author information

Authors and Affiliations

  1. Department of Mathematics, University of British Columbia, Vancouver, BC, V6T 1Z2, Canada

    Fred Brauer

Authors
  1. Fred Brauer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fred Brauer .

Editor information

Editors and Affiliations

  1. School of Public Health, Georgia State University, Atlanta, Georgia, USA

    Gerardo Chowell

  2. Department of Mathematics, Tulane University, New Orleans, Louisiana, USA

    James M. Hyman

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Brauer, F. (2016). Age of Infection Epidemic Models. In: Chowell, G., Hyman, J. (eds) Mathematical and Statistical Modeling for Emerging and Re-emerging Infectious Diseases. Springer, Cham. https://doi.org/10.1007/978-3-319-40413-4_13

Download citation

Publish with us

Policies and ethics

Search

Navigation