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A note on fractional linear pure birth and pure death processes in epidemic models

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  • Garra, Roberto
  • Polito, Federico

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.

Suggested Citation

  • Garra, Roberto & Polito, Federico, 2011. "A note on fractional linear pure birth and pure death processes in epidemic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3704-3709.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:21:p:3704-3709
    DOI: 10.1016/j.physa.2011.06.005
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    References listed on IDEAS

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    1. Yosihiko Ogata, 1998. "Space-Time Point-Process Models for Earthquake Occurrences," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 379-402, June.
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    1. Md Rafiul Islam & Angela Peace & Daniel Medina & Tamer Oraby, 2020. "Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles," IJERPH, MDPI, vol. 17(6), pages 1-19, March.

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