Random contact processes, snowball sampling and factorial series distributions

A contact process first posed as a random mapping problem is discussed together with a model for the spread of a rumour through an archaic telephone system. Snowball sampling and the well-known Reed–Frost chain binomial model are also commented on. Our main interest and emphasis is on distributional properties of discrete-time models. Simple combinatorial arguments are used along with a class of discrete distributions originally proposed for catch–recapture sampling.