Effect of social group dynamics on contagion

Zhenyuan Zhao, J. P. Calderón, Chen Xu, Guannan Zhao, Dan Fenn, Didier Sornette, Riley Crane, Pak Ming Hui, and Neil F. Johnson
Phys. Rev. E 81, 056107 – Published 25 May 2010

Abstract

Despite the many works on contagion phenomena in both well-mixed systems and heterogeneous networks, there is still a lack of understanding of the intermediate regime where social group structures evolve on a similar time scale to individual-level transmission. We address this question by considering the process of transmission through a model population comprising social groups which follow simple dynamical rules for growth and breakup. Despite the simplicity of our model, the profiles produced bear a striking resemblance to a wide variety of real-world examples—in particular, empirical data that we have obtained for social (i.e., YouTube), financial (i.e., currency markets), and biological (i.e., colds in schools) systems. The observation of multiple resurgent peaks and abnormal decay times is qualitatively reproduced within the model simply by varying the time scales for group coalescence and fragmentation. We provide an approximate analytic treatment of the system and highlight a novel transition which arises as a result of the social group dynamics.

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  • Received 16 October 2009

DOI:https://doi.org/10.1103/PhysRevE.81.056107

©2010 American Physical Society

Authors & Affiliations

Zhenyuan Zhao1, J. P. Calderón2, Chen Xu3, Guannan Zhao1, Dan Fenn4, Didier Sornette5, Riley Crane5, Pak Ming Hui6, and Neil F. Johnson1

  • 1Physics Department, University of Miami, Coral Gables, Florida 33126, USA
  • 2Industrial Engineering Department, Universidad de Los Andes, Bogota, Colombia
  • 3School of Physical Science and Technology, Soochow University, Suzhou 215006, People’s Republic of China
  • 4Oxford Centre for Industrial and Applied Maths, Oxford University, Oxford OX1 3PU, United Kingdom
  • 5ETH Zurich, D-MTEC, Kreuzplatz 5, 8001 Zurich, Switzerland
  • 6Department of Physics, The Chinese University of Hong Kong, Shatin, Hong Kong

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Issue

Vol. 81, Iss. 5 — May 2010

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