Susceptible-infected-susceptible model on networks with eigenvector localization

Zong-Wen Wei and Bing-Hong Wang
Phys. Rev. E 101, 042310 – Published 27 April 2020

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 the 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.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Received 16 July 2019
  • Revised 6 November 2019
  • Accepted 26 March 2020

DOI:https://doi.org/10.1103/PhysRevE.101.042310

©2020 American Physical Society

Physics Subject Headings (PhySH)

NetworksStatistical Physics & ThermodynamicsInterdisciplinary Physics

Authors & Affiliations

Zong-Wen Wei1,* and Bing-Hong Wang2,†

  • 1Guangdong Province Key Laboratory of Popular High Performance Computers, College of Computer Science and Software Engineering, Shenzhen University, Shenzhen 518060, China
  • 2Department of Modern Physics, University of Science and Technology of China, Hefei 230027, China

  • *wbravo@mail.ustc.edu.cn
  • bhwang@ustc.edu.cn

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 101, Iss. 4 — April 2020

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×