The FT provides a tool for simulating the spread of an infectious disease. Though they caution that the model is not based on any complex algorithm, simplicity should not be mistaken for error. Even a simple routing scheme like this one can capture many of the dynamics of the underlying process, as it doesn't take a particularly complicated network to emulate the real thing.
I would guess that they have a few preprogrammed routes which travelers randomly follow, coupled with a random probability of becoming infected after coming in contact with a sick person. I suppose the whole thing could boil down to a few Markov chains if you wanted to get away from nice infographics - but this is an excellent and informative example of translating that math into a tangible and accessible exercise.
The tool is very interesting, in a morbid way, though I will point out that the highest possible infection rate is 101%, while the highest possible mortality rate is 99% (yes, I checked).