  We present a theory for the laboratory and epidemiological data for
incubation times in infectious prion diseases. The central feature of our model
is that slow growth of misfolded protein-aggregates from small initial seeds
controls the `latent' or `lag' phase, whereas aggregate-fissioning and
subsequent spreading leads to an exponential growth or doubling phase. Such a
general framework can account for many features of prion diseases including the
striking reproducibility of incubation times when high doses are inoculated
into lab animals. Broad incubation time distributions arise for low infectious
dose, while our calculated distributions narrow to sharply defined onset times
with increased dose. We apply our distributions to epidemiological vCJD data
and extract estimates of incubation times.
