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

M. Saeedian1, M. Khalighi1, N. Azimi-Tafreshi2, G. R. Jafari1,3,4, and M. Ausloos5,6,7

  • 1Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran
  • 2Physics Department, Institute for Advanced Studies in Basic Sciences, 45195-1159 Zanjan, Iran
  • 3School of Biological Sciences, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran
  • 4Center for Network Science, Central European University, H-1051 Budapest, Hungary
  • 5GRAPES, rue de la Belle Jardinière 483, B-4031 Angleur, Belgium
  • 6School of Management, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom
  • 7eHumanities group, Royal Netherlands Academy of Arts and Sciences, Joan Muyskenweg 25, 1096 CJ, Amsterdam, The Netherlands

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Phys. Rev. E 95, 022409 – Published 21 February, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.022409

Abstract

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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Outline

Information

Phys. Rev. E 95, 022409– Published 21 February, 2017
  • Received 5 April 2016
  • Revised 20 December 2016

©2017 American Physical Society

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