Propagation dynamics on networks featuring complex topologies

TL;DR

This paper develops a mean-field model to analyze how complex network topologies influence propagation dynamics, providing analytical insights into epidemic thresholds and equilibria in structured social networks.

Contribution

It introduces a coupled mean-field approach that links network dynamics with topological patterns, yielding analytical solutions for epidemic thresholds and equilibria in complex networks.

Findings

Analytical epidemic thresholds depend on network topology.

Clustered networks exhibit higher epidemic thresholds than random networks.

Model predictions align well with numerical simulations.

Abstract

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (nodes, vertices, individuals...) on the one hand and their recurrent topological patterns (subgraphs, groups...) on the other hand. In a SIS model of epidemic spread on social networks with community structure, this approach yields a set of ODEs for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce random networks behavior in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.