Epidemic threshold and topological structure of susceptible-infectious-susceptible epidemics in adaptive networks

Dongchao Guo, Stojan Trajanovski, Ruud van de Bovenkamp, Huijuan Wang, and Piet Van Mieghem
Phys. Rev. E 88, 042802 – Published 4 October 2013

Abstract

The interplay between disease dynamics on a network and the dynamics of the structure of that network characterizes many real-world systems of contacts. A continuous-time adaptive susceptible-infectious-susceptible (ASIS) model is introduced in order to investigate this interaction, where a susceptible node avoids infections by breaking its links to its infected neighbors while it enhances the connections with other susceptible nodes by creating links to them. When the initial topology of the network is a complete graph, an exact solution to the average metastable-state fraction of infected nodes is derived without resorting to any mean-field approximation. A linear scaling law of the epidemic threshold τc as a function of the effective link-breaking rate ω is found. Furthermore, the bifurcation nature of the metastable fraction of infected nodes of the ASIS model is explained. The metastable-state topology shows high connectivity and low modularity in two regions of the τ,ω plane for any effective infection rate τ>τc: (i) a “strongly adaptive” region with very high ω and (ii) a “weakly adaptive” region with very low ω. These two regions are separated from the other half-open elliptical-like regions of low connectivity and high modularity in a contour-line-like way. Our results indicate that the adaptation of the topology in response to disease dynamics suppresses the infection, while it promotes the network evolution towards a topology that exhibits assortative mixing, modularity, and a binomial-like degree distribution.

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  • Received 26 April 2013

DOI:https://doi.org/10.1103/PhysRevE.88.042802

©2013 American Physical Society

Authors & Affiliations

Dongchao Guo1,2,*, Stojan Trajanovski1,†, Ruud van de Bovenkamp1, Huijuan Wang1, and Piet Van Mieghem1

  • 1Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands
  • 2Institute of Information Science, Beijing Jiaotong University, 100044 Beijing, People's Republic of China

  • *08112070@bjtu.edu.cn
  • s.trajanovski@tudelft.nl

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Vol. 88, Iss. 4 — October 2013

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