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Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model

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journal contribution
posted on 30.03.2017, 10:40 by M. Saeedian, M. Khalighi, N. Azimi-Tafreshi, G. R. Jafari, Marcel Ausloos
Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by a non-Markovian dynamics: memory effects play an essential role in the spreading of diseases. Including memory effects in the susceptible-infected-recovered (SIR) epidemic model seems very appropriate for such an investigation. Thus, the memory prone SIR model dynamics is investigated using fractional derivatives. The decay of long-range memory, taken as a power-law function, is directly controlled by the order of the fractional derivatives in the corresponding nonlinear fractional differential evolution equations. Here we assume "fully mixed" approximation and show that the epidemic threshold is shifted to higher values than those for the memoryless system, depending on this memory "length" decay exponent. We also consider the SIR model on structured networks and study the effect of topology on threshold points in a non-Markovian dynamics. Furthermore, the lack of access to the precise information about the initial conditions or the past events plays a very relevant role in the correct estimation or prediction of the epidemic evolution. Such a "constraint" is analyzed and discussed.

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Citation

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 2017, 95 (2), 022409

Author affiliation

/Organisation/COLLEGE OF SOCIAL SCIENCES, ARTS AND HUMANITIES/School of Management

Version

VoR (Version of Record)

Published in

Physical Review E - Statistical

Publisher

American Physical Society

issn

1539-3755

eissn

1550-2376

Acceptance date

20/12/2016

Copyright date

2017

Available date

30/03/2017

Publisher version

https://journals.aps.org/pre/abstract/10.1103/PhysRevE.95.022409

Language

en

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