The Maki–Thompson rumour model: a detailed analysis

The general solution for stochastic rumour models has recently been derived by Pearce (Math. Comput. Modelling. (2000)) for both the Daley–Kendall and Maki–Thompson cases. This paper concentrates on the simpler Maki–Thompson model, which presents some particular problems of its own. A general solution is set out, and illustrated by an example starting with 1 spreader and 2 ignorants; in this case, the probabilities of 2, 1 and 0 surviving ignorants are 0, 1/4 and 3/4 respectively.