One of the homework problems examined the pioneering work in epidemiology of Kermack and McKendrick. This study simplified the SIR model (for susceptibles, infecteds, and recovered or dead) to a one-dimensional dynamical system. There are many classes of epidemic models that have been developed, including ones for gonorrhea, measles, and HIV/AIDS. Your project is to examine one or more of these models in some detail. You should compare the mathematical model to actual data to test the strengths and weaknesses of these models. The literature is vast for this subject, so you need to decide on a specific disease (or two if you want to contrast models), then present work on models for this disease. You should probably begin with the material in J. D. Murray's book in the references below. I'm also including a couple websites, which may or may not be useful

References:

1. M. Braun (1983) Differential Equations and Their Applications, Springer, New York, p.463ff.
2. L. Edelstein-Keshet (1988) Mathematical Models in Biology, Random House, New York.
3. W. O. Kermack and A. G. McKendrick (1927) Contributions to the mathematical theory of epidemics - I. Proc. Roy. Soc. 115A, 700.
4. J. D. Murray (1989) Mathematical Biology, Chapter 19, Springer, New York.