Oh dear. I found a new (to me) toy, STEM: Spatio-Temporal Epidemological/Event Modeler. It comes built-in with a simulation of what would happen if the 1918 Spanish Flu outbreak happened in 2000, with various starting points. You can create your own SIR/SIS/SIER virus and set them loose, while they infect the entire world by way of bird migratory patterns, air traffic, etc. What's more, they've released the source code, allowing a whole new level of tinkering.
Full press release here.
For some background on the mathematics, see The Mathematics of Infectious Disease, by Herbert Hethcote.