Analysis of the susceptible-infected-susceptible epidemic dynamics in networks via the non-backtracking matrix

Naoki Masuda*, Victor M. Preciado, Masaki Ogura

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We study the stochastic susceptible-infected-susceptible model of epidemic processes on finite directed and weighted networks with arbitrary structure. We present a new lower bound on the exponential rate at which the probabilities of nodes being infected decay over time. This bound is directly related to the leading eigenvalue of a matrix that depends on the non-backtracking and incidence matrices of the network. The dimension of this matrix is N+M, where N and M are the number of nodes and edges, respectively. We show that this new lower bound improves on an existing bound corresponding to the so-called quenched mean-field theory. Although the bound obtained from a recently developed second-order moment-closure technique requires the computation of the leading eigenvalue of an N2× N2 matrix, we illustrate in our numerical simulations that the new bound is tighter, while being computationally less expensive for sparse networks. We also present the expression for the corresponding epidemic threshold in terms of the adjacency matrix of the line graph and the non-backtracking matrix of the given network.

Original languageEnglish
Pages (from-to)214-230
Number of pages17
JournalIMA Journal of Applied Mathematics
Volume85
Issue number2
DOIs
Publication statusPublished - 2020 Apr 26
Externally publishedYes

Keywords

  • epidemic processes
  • epidemic threshold
  • networks
  • non-backtracking matrix
  • stochastic processes

ASJC Scopus subject areas

  • Applied Mathematics

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