also determines the ease with which control policies can control an epidemic. Once a significant proportion of the population has been infected, not all contacts of an infected individual will be with susceptible people. Infection can now continue only because new births replenish the susceptible population. Eventually an endemic equilibrium is reached where every infected person infects one other individual on average. Heterogeneity in host susceptibility, infectiousness, human contact patterns and in the genetic composition of pathogen populations introduces substantial additional complexity into this picture, however - and into the models required to model real diseases realistically. This chapter concludes with a brief review of the recent application of mathematical models to a wide range of emerging human or animal epidemics, most notably the spread of HIV in Africa, the 2001 foot and mouth epidemic in British livestock, bioterrorism threats such as smallpox, the SARS epidemics in 2003 and most recently the use of modelling as a tool for influenza pandemic preparedness planning.