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 R0, 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.
*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.