Epidemic spreading in correlated complex networks

TL;DR

This paper investigates how correlations in complex networks influence epidemic spreading, revealing that the epidemic threshold depends on the network's connectivity matrix eigenvalues, supported by simulations.

Contribution

It introduces a model analyzing epidemic thresholds in correlated networks, highlighting the role of connectivity correlations and eigenvalues, which was not addressed in prior uncorrelated models.

Findings

Epidemic threshold inversely proportional to the largest eigenvalue of the connectivity matrix

Correlations among node connectivities significantly affect epidemic dynamics

Numerical simulations support the analytical predictions

Abstract

We study a dynamical model of epidemic spreading on complex networks in which there are explicit correlations among the node's connectivities. For the case of Markovian complex networks, showing only correlations between pairs of nodes, we find an epidemic threshold inversely proportional to the largest eigenvalue of the connectivity matrix that gives the average number of links that from a node with connectivity $k$ go to nodes with connectivity $k'$. Numerical simulations on a correlated growing network model provide support for our conclusions.