In this thesis, three stochastic epidemic models for intervention for emerging diseases are considered. The models are variants of real-time, responsive intervention, based upon observing diagnosed cases and targeting intervention towards individuals they have infected or are likely to have infected, be they housemates or named contacts. These models are: (i) a local tracing model for a disease spreading amongst a community of households, wherein intervention (vaccination and/or isolation) is directed towards housemates of diagnosed individuals, (ii) a contact tracing model for a disease spreading amongst a homogeneously-mixing population, with isolation of traced contacts of a diagnosed individual, (iii) a local tracing and contact tracing model for a disease spreading amongst a community of households, with intervention directed towards housemates of both diagnosed and traced individuals. These are quantified by deriving threshold parameters that determine whether the disease will infect a few individuals or a sizeable proportion of the population, as well as probabilities for such events occurring.