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The Kermack-McKendrick Model of Epidemiology

This is the paper that contains the most basic models and results for
epidmiology. The paper, and the followups contain many more
advanced models as well.
They derive the basic epidemiological equations and get at the
notion
of reproductive number for a disease. This is the most central
result
in epidemiology and a tour de force in theoretical ecology. The model
that gets the most attention is the SIR model (sustainable, infective,
removed). We will derive
the model in detail, and give careful consideration to the assumptions
underlying the model.

In analyzing the model, we will emphasize the role played by R_{0},
the reproductive number. This is a concept that plays an
important role throughout population biology. We will alsoderive
and ephasize the threshold theorem and try and undertsand its
importance.
Reading the piece by Anderson will put the results
into context, and give an introduction into the more modern literature.
Although only part I is required reading, all parts will
be available for copying, and we will discuss endemicity in class.

The Diekmann and Heesterbeek is a nice recent survey which is somewhat
mathematical.
## References

* means required reading
*Anderson, R.M. 1991. Discussion: The Kermack-McKendrick epidemic
threshold
theorem. Bull. Math. Biol. 53:3-32.

Diekmann, O.; Heesterbeek.J.A.P. 2000. Mathematical
epidemiology of infectious diseases : model building, analysis, and
interpretation. New York John Wiley, New York.

*Kermack,
W.O. and McKendrick, A.G. 1927 Contributions to the mathematical theory
of epidemics. I. Proceedings of the Royal Society 115A:700-721.

Kermack,
W.O. and McKendrick, A.G. 1932 Contributions to the mathematical theory
of epidemics. II. The problem of endemicity. Proceedings of the Royal
Society
138A:55-83.

Kermack,
W.O. and McKendrick, A.G. 1933 Contributions to the mathematical theory
of epidemics. III. Further studies of the problem of endemicity.
Proceedings
of the Royal Society 141A:94-122.