This week, That’s Maths (TM006) describes the use of mathematical models to study the spread of infections like the SARS epidemic and swine flu.
Simple models such as the SIR model of Kermack and McKendrick (1927) can simulate the broad features of epidemics, but much more sophisticated models have been developed using the same approach.
For an elementary introduction to the mthematics of modelling infectious diseases, see Epidemic Modelling, by D. J. Daley and J. Gani, Cambridge Univ. Press, 1999.