In this note we highlight the role of fractional linear birth and lineardeath processes recently studied in \citet{sakhno} and \citet{pol}, in relationto epidemic models with empirical power law distribution of the events. Takinginspiration from a formal analogy between the equation of self consistency ofthe epidemic type aftershock sequences (ETAS) model, and the fractionaldifferential equation describing the mean value of fractional linear growthprocesses, we show some interesting applications of fractional modelling tostudy \textit{ab initio} epidemic processes without the assumption of anyempirical distribution. We also show that, in the frame of fractionalmodelling, subcritical regimes can be linked to linear fractional deathprocesses and supercritical regimes to linear fractional birth processes.Moreover we discuss a simple toy model to underline the possible application ofthese stochastic growth models to more general epidemic phenomena such astumoral growth.
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