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Explicit non-Markovian susceptible-infected-susceptible mean-field epidemic threshold for Weibull and Gamma infections but Poisson curings

P. Van Mieghem and Qiang Liu
Phys. Rev. E 100, 022317 – Published 26 August 2019

Abstract

Although non-Markovian processes are considerably more complicated to analyze, real-world epidemics are likely non-Markovian, because the infection time is not always exponentially distributed. Here, we present analytic expressions of the epidemic threshold in a Weibull and a Gamma SIS epidemic on any network, where the infection time is Weibull, respectively, Gamma, but the recovery time is exponential. The theory is compared with precise simulations. The mean-field non-Markovian epidemic thresholds, both for a Weibull and Gamma infection time, are physically similar and interpreted via the occurrence time of an infection during a healthy period of each node in the graph. Our theory couples the type of a viral item, specified by a shape parameter of the Weibull or Gamma distribution, to its corresponding network-wide endemic spreading power, which is specified by the mean-field non-Markovian epidemic threshold in any network.

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  • Received 10 May 2019
  • Revised 8 July 2019

DOI:https://doi.org/10.1103/PhysRevE.100.022317

©2019 American Physical Society

Physics Subject Headings (PhySH)

Interdisciplinary Physics

Authors & Affiliations

P. Van Mieghem* and Qiang Liu

  • Faculty of Electrical Engineering, Mathematics, and Computer Science, Delft University of Technology, Delft, The Netherlands

  • *P.F.A.VanMieghem@tudelft.nl
  • Q.L.Liu@tudelft.nl

Article Text

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Issue

Vol. 100, Iss. 2 — August 2019

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