An integral equation model of Kermack-McKendrick type is proposed for describing the dynamics of an infectious disease invading a susceptible population. Modifications of the model, including control strategies based on the isolation of infectious individuals and targeted vaccination, are described. In the model the incidence of infection is structured according to the location of exposure, and parameterization requires some knowledge of the infectivity kernel and the initial rate of exponential increase of cases. The model was motivated by the risk to a community from the global epidemic of severe acute respiratory syndrome (SARS) in 2003, and the prospect of future epidemics of emerging infections. It is also applicable where terrorists may use an infectious agent such as smallpox as a weapon.