Skip to main content

Modeling Influenza: Pandemics and Seasonal Epidemics

  • Chapter

Part of the Lecture Notes in Mathematics book series (LNMBIOS,volume 1945)

We describe and analyze compartmental models for influenza, including pre-epidemic vaccination and antiviral treatment. The analysis is based on the final size relation for compartmental epidemic models. We consider models of increasing complexity and compare their predictions using parameter values appropriate to the 1957 pandemic.

Keywords

  • Antiviral Treatment
  • Reproduction Number
  • Disease Death Rate
  • Basic Reproduction Number
  • Disease Case

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   69.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   89.99
Price excludes VAT (Canada)
  • Compact, lightweight 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M.E. Alexander, C.S. Bowman, Z. Feng, M. Gardam, S.M. Moghadas, G. Röst, J. Wu & P. Yan, Emergence of drug resistance: implications for antiviral control of pandemic influenza, Proc. R. Soc. B 274, 1675–1684 (2007)

    CrossRef  Google Scholar 

  2. J. Arino, F. Brauer, P. van den Driessche, J. Watmough & J. Wu, Simple models for containment of a pandemic, J. R. Soc. Interface 3, 453–457 (2006)

    CrossRef  Google Scholar 

  3. J. Arino, F. Brauer, P. van den Driessche, J. Watmough & J. Wu, A model for influenza with vaccination and antiviral treatment, J. Theor. Biol., in press, available online, doi: 10.1016/j.jtbi.2008.02.026

    Google Scholar 

  4. S. Cauchemez, F. Carrat, C. Viboud, A.J. Valleron & P.Y. Boëlle, A Bayesian MCMC approach to study transmission of influenza: application to household longitudinal data, Stat. In Med. 232, 3469–3487 (2004)

    CrossRef  Google Scholar 

  5. L.R. Elveback, J.P. Fox, E. Ackerman, A. Langworthy, M. Boyd & L. Gatewood, An influenza simulation model for immunization studies, Am. J. Epidem. 103, 152–165 (1976)

    Google Scholar 

  6. N.M. Ferguson, D.A.T. Cummings, S. Cauchemez, C. Fraser, S. Riley, A. Meeyai, S. Iamsirithaworn & D.S. Burke, Strategies for containing an emerging influenza pandemic in Southeast Asia, Nature 437, 209–214 (2005)

    CrossRef  Google Scholar 

  7. N.M. Ferguson, D.A.T. Cummings, C. Fraser, J.C. Cajka, P.C. Cooley & D.S. Burke, Strategies for mitigating an influenza pandemic, Nature 442, 448–452 (2006)

    CrossRef  Google Scholar 

  8. M. Gardam, D. Liang, S.M. Moghadas, J. Wu, Q. Zeng & H. Zhu, The impact of prophylaxis of healthcare workers on influenza pandemic burden, J. R. Soc. Interface 4, 727–734 (2007)

    CrossRef  Google Scholar 

  9. T.C. Germann, K. Kadau, I.M. Longini & C.A. Macken, Mitigation strategies for pandemic influenza in the United States, Proc. Natl. Acad. Sci. U. S. A. 103, 5935–5940 (2006)

    CrossRef  Google Scholar 

  10. M. Lipsitch, T. Cohen, M. Murray & B.R. Levin, Antiviral resistance and the control of pandemic influenza, PLoS Med. 4, 111–121 (2007)

    CrossRef  Google Scholar 

  11. I.M. Longini, M.E. Halloran, A. Nizam & Y. Yang, Containing pandemic influenza with antiviral agents, Am. J. Epidem. 159, 623–633 (2004)

    CrossRef  Google Scholar 

  12. I.M. Longini, A. Nizam, S. Xu, K. Ungchusak, W. Hanshaoworakul, D.T. Cummings & M.E. Halloran, Containing pandemic influenza at the source, Science 309, 623–633 (2004)

    Google Scholar 

  13. A. Nold, Heterogeneity in disease transmission modeling, Math. Biosc. 52, 227–240 (1980)

    CrossRef  MATH  MathSciNet  Google Scholar 

  14. R.R. Regoes & S. Bonhoeffer, Emergence of drug-resistant influenza virus: population dynamical considerations, Science 312, 389–391 (2006)

    CrossRef  Google Scholar 

  15. N.I. Stillianakis, A.S. Perelson & F.G. Hayden, Emergence of drug resistance during an influenza epidemic: insights from a mathematical model, J. Infect. Dis. 177, 863–873 (1998)

    Google Scholar 

  16. P. van den Driessche & J. Watmough, Reproduction numbers and subthreshold endemic equilibria for compartmental models of disease transmission, Math. Biosc. 180, 29–48 (2002)

    CrossRef  MATH  Google Scholar 

  17. R. Welliver, A.S. Monto, O. Carewicz, E. Schatteman, M. Hassman, M.J. Hedrick, H.C. Jackson, L. Huson, P. Ward & J.S. Oxford, Effectiveness of oseltamivir in preventing influenza in household contacts: a randomized controlled trial, JAMA 285, 748–754 (2001)

    CrossRef  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Brauer, F. (2008). Modeling Influenza: Pandemics and Seasonal Epidemics. In: Brauer, F., van den Driessche, P., Wu, J. (eds) Mathematical Epidemiology. Lecture Notes in Mathematics, vol 1945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78911-6_12

Download citation