Zombies are a staple of modern popular culture, and appear in a variety of forms, including the traditional slow-moving, unintelligent zombie hordes and less common fast-moving – and perhaps intelligent – zombies. The common theme in media featuring zombies is the the zombie infection, which may affect either the living or the deceased, or both. It is generally agreed that this infection is passed from zombie to non-zombie by means of a scratch or bite, and infection always leads to a transformation into a zombie. (In some more modern interpretations, this transformation may be reversible.)
The spread of the zombie infection is an interesting problem to model mathematically. There are many factors to consider: the chances of a non-zombie becoming infected in an interaction with a zombie; the rate at which interactions between non-zombies and zombies occur; the spread the zombie horde from place to place; and the “critical mass” of the zombie horde at which point there is insufficient food for all zombies. We can model parts of this problem in isolation, with some simplifying assumptions.