In this note we highlight the role of fractional linear birth and linear death processes, recently studied in Orsingher et al. (2010) [5] and Orsingher and Polito (2010) [6], in relation to epidemic models with empirical power law distribution of the events. Taking inspiration from a formal analogy between the equation for 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 in studying ab initio epidemic processes without the assumption of any empirical distribution. We also show that, in the framework 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 in order to underline the possible application of these stochastic growth models to more general epidemic phenomena such as tumoral growth. (C) 2011 Elsevier B.V. All rights reserved.
A note on fractional linear pure birth and pure death processes in epidemic models / Garra, Roberto; Polito, Federico. - In: PHYSICA. A. - ISSN 0378-4371. - STAMPA. - 390:21-22(2011), pp. 3704-3709. [10.1016/j.physa.2011.06.005]
A note on fractional linear pure birth and pure death processes in epidemic models
Roberto Garra;POLITO, FEDERICO
2011
Abstract
In this note we highlight the role of fractional linear birth and linear death processes, recently studied in Orsingher et al. (2010) [5] and Orsingher and Polito (2010) [6], in relation to epidemic models with empirical power law distribution of the events. Taking inspiration from a formal analogy between the equation for 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 in studying ab initio epidemic processes without the assumption of any empirical distribution. We also show that, in the framework 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 in order to underline the possible application of these stochastic growth models to more general epidemic phenomena such as tumoral growth. (C) 2011 Elsevier B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.