Second-order mean-field susceptible-infected-susceptible epidemic threshold

E. Cator and P. Van Mieghem
Phys. Rev. E 85, 056111 – Published 14 May 2012

Abstract

Given the adjacency matrix A of a network, we present a second-order mean-field expansion that improves on the first-order N-intertwined susceptible-infected-susceptible (SIS) epidemic model. Unexpectedly, we found that, in contrast to first-order, second-order mean-field theory is not always possible: the network size N should be large enough. Under the assumption of large N, we show that the crucial and characterizing quantity, the SIS epidemic threshold τc, obeys an eigenvalue equation, more complex than the one in the first-order N-intertwined model. However, the resulting epidemic threshold is more accurate: τc(2)=τc(1)+O(τc(1)N), where the first-order epidemic threshold is τc(1)=1λ1(A) and where λ1(A) is the spectral radius of the adjacency matrix A.

  • Figure
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  • Received 23 December 2011

DOI:https://doi.org/10.1103/PhysRevE.85.056111

©2012 American Physical Society

Authors & Affiliations

E. Cator* and P. Van Mieghem

  • Faculty of Electrical Engineering, Mathematics and Computer Science, P.O. Box 5031, 2600 GA Delft, The Netherlands

  • *e.a.cator@tudelft.nl
  • p.f.a.vanmieghem@tudelft.nl

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Issue

Vol. 85, Iss. 5 — May 2012

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