These models simulate potentially unlimited growth characterised by a reproduction rate, ρ, parameter. The simulation can either be deterministic or modelled as a Poisson process.
A finite population with initial infectious cases. Individuals may recover but can get reinfected. There are two parameters here so that infection and recovery can be independently controlled. Randomness can be introduced by a Binomial distribution.
Here are links to a few other epidemiological simulation pages on the web. Mostly they are more complicated than the simple ones above, and may use different names and parameterisation schemes.