  We consider the spread of a Susceptible-Infected-Recovered (SIR) disease
through finite populations and derive an expression for the final size
distribution. Our derivation allows arbitrary distributions of the number of
transmissions caused by an infected individual. We show how this calculation
can be used to infer parameters of the infectious disease through observations
in multiple small populations. The inference suffers from some identifiability
difficulties, and it requires many observations to distinguish between
parameter combinations that correspond to the same reproductive number.
