There are many Epidemic model. Some use simple stochastic compartmental models based on a Master equation (see Simple contagion). See Epidemics on networks, for models that include the underlying network structure.
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