Keywords: Network science, Epidemiology

Cascades on Networks. There Watt's cascade model is described, among other things.

See Mason and Gleeson "Dynamical systems on networks"

Types of contagions

For Simple contagions, a node can get infected by simple exposure to another infected node (possibly with a certain probability or rate). These are mostly compartmental models, and their extensions are used to model mostly biological contagions (like infectious diseases), as well as some IT contagions (like computer viruses)

For Complex contagions, nodes get infected by more complex processes, often involving several other nodes. These are often used to model more complicated social contagions and phenomena. See Social dynamics

See also wiki page: Complex contagion