  We suggest an explanation of typical incubation times statistical features
based on the universal behavior of exit times for diffusion models. We give a
mathematically rigorous proof of the characteristic right skewness of the
incubation time distribution for very general one-dimensional diffusion models.
Imposing natural simple conditions on the drift coefficient, we also study
these diffusion models under the assumption of noise smallness and show that
the limiting exit time distributions in the limit of vanishing noise are
Gaussian and Gumbel. Thus they match the existing data as well as the other
existing models do. The character of our models, however, allows us to argue
that the features of the exit time distributions that we describe are universal
and manifest themselves in various other situations where the times involved
can be described as detection or halting times, for example, response times
studied in psychology.
