  In this note we highlight the role of fractional linear birth and linear
death processes recently studied in \citet{sakhno} and \citet{pol}, in relation
to epidemic models with empirical power law distribution of the events. Taking
inspiration from a formal analogy between the equation of self consistency of
the epidemic type aftershock sequences (ETAS) model, and the fractional
differential equation describing the mean value of fractional linear growth
processes, we show some interesting applications of fractional modelling to
study \textit{ab initio} epidemic processes without the assumption of any
empirical distribution. We also show that, in the frame of fractional
modelling, subcritical regimes can be linked to linear fractional death
processes and supercritical regimes to linear fractional birth processes.
Moreover we discuss a simple toy model to underline the possible application of
these stochastic growth models to more general epidemic phenomena such as
tumoral growth.
