Susceptible-infected-susceptible model on networks with eigenvector localization

Abstract

It is a longstanding debate on the absence of threshold for susceptible-infected-susceptible (SIS) model on networks with finite second order moment of degree distribution. The eigenvector localization of the adjacency matrix for a network gives rise to the inactive Griffiths phase featuring slow decay of the activity localized around highly connected nodes due to the dynamical fluctuation. We show how it dramatically changes our understanding of SIS model, opening up new possibilities for the debate. We derive the critical condition for Griffiths to active phase transition: on average, an infected node can further infect another one in the characteristic lifespan of the star subgraph composed of the node and its nearest neighbors. The system approaches the critical point of avoiding the irreversible dynamical fluctuation and the trap of absorbing state. As a signature of the phase transition, the infection density of a node is not only proportional to its degree, but also proportional to the exponentially growing lifespan of the star. And the divergence of the average lifespan of the stars is responsible for the vanishing threshold in the thermodynamic limit. The eigenvector localization exponentially reinforces the infection of highly connected nodes, while it inversely suppresses the infection of small-degree nodes.

References in corpus (9)

• Thresholds for epidemic spreading in networks
• Unification of theoretical approaches for epidemic spreading on complex networks
• Epidemic thresholds of the Susceptible-Infected-Susceptible model on networks: A comparison of numerical and theoretical results
• Griffiths phases on complex networks
• Spectra of random graphs with arbitrary expected degrees
• Solving the Dynamic Correlation Problem of the Susceptible-Infected-Susceptible Model on Networks
• Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects
• Eigenvector localization in real networks and its implications for epidemic spreading
• Multiple phase transitions of the susceptible-infected-susceptible epidemic model on complex networks

Cited by in corpus (2)

• Simple quasistationary method for simulations of epidemic processes with localized states
• Hierarchical Coarse-grained Approach to the Duration-dependent Spreading Dynamics in Complex Networks