How mathematics can make epidemics history

An exceedingly simple model, the Galton-Watson process, was introduced in 1875 and exhibits the behaviour of the 'reproduction number'. If the average number of offspring in a Galton-Watson process is less than 1, the population dies off with probability 1, with thin tails on the number of generations before extinction; if it's more than 1, it has a positive chance to survive forever.