When stochastic effects, such as those inevitably found in nature, are included, the threshold at R 0 = 1 may be disturbed. This includes assumptions about the distribution of transition times (assumed to be exponential in most models) as well as variations in individual parameters. Heffernan and Wahl [28] derived improved estimates of R 0 for situations in which information about the dispersal of transition times is available to the clinical or epidemiological practitioner. Rather than rederiving R 0 for a number of models (SIR, SEIR, etc.), they introduce a "correction factor", φ: the ratio of R 0 when the lifetimes are nonexponentially distributed to the value of R 0 that would be calculated assuming exponential lifetimes. They were able to derive limiting values of φ and used this to gauge the sensitivity of R 0 to dispersion in the underlying distributions.