Ever since the pattern of localised extinction associated with measles
was discovered by Bartlett in 1957, modellers have been attempting to capture
this phenomenon. Recently the use of constant infectious and incubation
periods, rather than the more convenient exponential forms, has been presented
as a simple means of obtaining realistic persistence levels. However this
result appears at odds with rigorous mathematical theory -- here we reconcile
these differences. Using a deterministic approach we parameterise a variety
of models to fit the observed biennial attractor, thus determining the
level of seasonality by the choice of model. We can then compare fairly
the persistence of the stochastic versions of these models using the `best-fit'
parameters. Finally we consider the differences between the observed fade-out
pattern and the more theoretically appealing first passage time.