Invasion of diseases into new territory is a worldwide problem. Examples include West Nile fever in the US, HIV in Africa and Asia, and dengue in Latin America. Traditionally, the spatial spread of disease has been modeled using a local process, diffusion, to model dispersal. However, if dispersal is non-local, diffusion can greatly underestimate speeds of invasion. In this talk, I will discuss integrodifferential-equation models that incorporate knowledge about the dispersal of disease propagules and infected hosts to describe disease infection.