Analysis of the susceptibleinfectedsusceptible epidemic dynamics in networks via the nonbacktracking matrix
Abstract
We study the stochastic susceptibleinfectedsusceptible 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 nonbacktracking 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 socalled quenched meanfield theory. Although the bound obtained from a recently developed secondorder momentclosure technique requires the computation of the leading eigenvalue of an N^2 x N^2 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 nonbacktracking matrix of the given network.
 Publication:

arXiv eprints
 Pub Date:
 June 2019
 arXiv:
 arXiv:1906.04269
 Bibcode:
 2019arXiv190604269M
 Keywords:

 Physics  Physics and Society;
 Computer Science  Social and Information Networks
 EPrint:
 1 figure