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A Light Introduction to Modelling Recurrent Epidemics

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Mathematical Epidemiology

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

Epidemics of many infectious diseases occur periodically. Why?

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References

  1. M. S. Bartlett. Stochastic population models in ecology and epidemiology, volume 4 of Methuen’s Monographs on Applied Probability and Statistics. Spottiswoode, Ballantyne, London, 1960.

    MATH  Google Scholar 

  2. N. T. J. Bailey. The Mathematical Theory of Infectious Diseases and Its Applications. Hafner, New York, second edition, 1975.

    MATH  Google Scholar 

  3. R. M. Anderson and R. M. May. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford, 1991.

    Google Scholar 

  4. D. J. Daley and J. Gani. Epidemic modelling, an introduction, volume 15 of Cambridge: Studies in Mathematical Biology. Cambridge university press, Cambridge, 1999.

    MATH  Google Scholar 

  5. H. Andersson and T. Britton. Stochastic epidemic models and their statistical analysis, volume 151 of Lecture Notes in Statistics. Springer, New York, 2000.

    MATH  Google Scholar 

  6. O. Diekmann and J. A. P. Heesterbeek. Mathematical epidemiology of infectious diseases: model building, analysis and interpretation. Wiley Series in Mathematical and Computational Biology. Wiley, New York, 2000.

    Google Scholar 

  7. F. Brauer and C. Castillo-Chavez. Mathematical models in population biology and epidemiology, volume 40 of Texts in Applied Mathematics. Springer, New York, 2001.

    MATH  Google Scholar 

  8. D. Mollison, editor. Epidemic Models: Their Structure and Relation to Data. Publications of the Newton Institute. Cambridge University Press, Cambridge, 1995.

    MATH  Google Scholar 

  9. V. Isham and G. Medley, editors. Models for Infectious Human Diseases: Their Structure and Relation to Data. Publications of the Newton Institute. Cambridge University Press, Cambridge, 1996.

    MATH  Google Scholar 

  10. B. T. Grenfell and A. P. Dobson, editors. Ecology of Infectious Diseases in Natural Populations. Publications of the Newton Institute. Cambridge University Press, Cambridge, 1995.

    MATH  Google Scholar 

  11. C. Castillo-Chavez, with S. Blower, P. van den Driessche, D. Kirschner, and A-A. Yakubu, editors. Mathematical approaches for emerging and reemerging infectious diseases: an introduction, volume 125 of The IMA Volumes in Mathematics and Its Applications. Springer, New York, 2002.

    Google Scholar 

  12. C. Castillo-Chavez, with S. Blower, P. van den Driessche, D. Kirschner, and A-A. Yakubu, editors. Mathematical approaches for emerging and reemerging infectious diseases: models, methods and theory, volume 126 of The IMA Volumes in Mathematics and Its Applications. Springer, New York, 2002.

    Google Scholar 

  13. F. Brauer, P. van den Driessche and J. Wu, editors. Mathematical Epidemiology (this volume).

    Google Scholar 

  14. D. J. D. Earn. Mathematical modelling of recurrent epidemics. Pi in the Sky, 8:14–17, 2004.

    Google Scholar 

  15. W. O. Kermack and A. G. McKendrick. A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London Series A, 115:700–721, 1927.

    Article  Google Scholar 

  16. M. J. Keeling and C. A. Gilligan. Metapopulation dynamics of bubonic plague. Nature, 407:903–906, 2000.

    Article  Google Scholar 

  17. D. Hughes-Hallett, A. M. Gleason, P. F. Lock, D. E. Flath, S. P. Gordon, D. O. Lomen, D. Lovelock, W. G. McCallum, B. G. Osgood, D. Quinney, A. Pasquale, K. Rhea, J. Tecosky-Feldman, J. B. Thrash, and T. W. Tucker. Applied Calculus. Wiley, Toronto, second edition, 2002.

    Google Scholar 

  18. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery. Numerical Recipes in C. Cambridge University Press, Cambridge, second edition, 1992.

    MATH  Google Scholar 

  19. S. Wiggins. Introduction to applied nonlinear dynamical systems and chaos, volume 2 of Texts in Applied Mathematics. Springer, New York, 2 edition, 2003.

    MATH  Google Scholar 

  20. A. Korobeinikov and P. K. Maini. A Lyapunov function and global properties for SIR and SEIR epidemiological models with nonlinear incidence. Mathematical Biosciences and Engineering, 1(1):57–60, 2004.

    MATH  MathSciNet  Google Scholar 

  21. D. T. Gillespie. A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. Journal of Computational Physics, 22:403–434, 1976.

    Article  MathSciNet  Google Scholar 

  22. J. Gleick. Chaos. Abacus, London, 1987.

    MATH  Google Scholar 

  23. S. H. Strogatz. Nonlinear Dynamics and Chaos. Addison Wesley, New York, 1994.

    Google Scholar 

  24. D. J. D. Earn, P. Rohani, B. M. Bolker, and B. T. Grenfell. A simple model for complex dynamical transitions in epidemics. Science, 287(5453):667–670, 2000.

    Article  Google Scholar 

  25. C. T. Bauch and D. J. D. Earn. Transients and attractors in epidemics. Proceedings of the Royal Society of London Series B-Biological Sciences, 270(1524):1573–1578, 2003.

    Article  Google Scholar 

  26. J. Dushoff, J. B. Plotkin, S. A. Levin, and D. J. D. Earn. Dynamical resonance can account for seasonality of influenza epidemics. Proceedings of the National Academy of Sciences of the United States of America, 101(48):16915–16916, 2004.

    Article  Google Scholar 

  27. D. J. D. Earn, J. Dushoff, and S. A. Levin. Ecology and evolution of the flu. Trends in Ecology and Evolution, 17(7):334–340, 2002.

    Article  Google Scholar 

  28. IIDDA. The International Infectious Disease Data Archive, http://iidda.mcmaster.ca .

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    David J. D. Earn

Authors
  1. David J. D. Earn
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Editor information

Editors and Affiliations

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

    Fred Brauer

  2. Department of Mathematics and Statistics, University of Victoria, 3060 STN CSC, Victoria, B.C. V8W 3R4, Canada

    Pauline van den Driessche

  3. Center for Disease Modeling Department of Mathematics and Statistics, York University, Toronto, Ontario, M3J 1P3, Canada

    Jianhong Wu

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Earn, D.J.D. (2008). A Light Introduction to Modelling Recurrent 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_1

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