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Infection dynamics on spatial small-world network models

Bryan Iotti, Alberto Antonioni, Seth Bullock, Christian Darabos, Marco Tomassini, and Mario Giacobini
Phys. Rev. E 96, 052316 – Published 30 November 2017

Abstract

The study of complex networks, and in particular of social networks, has mostly concentrated on relational networks, abstracting the distance between nodes. Spatial networks are, however, extremely relevant in our daily lives, and a large body of research exists to show that the distances between nodes greatly influence the cost and probability of establishing and maintaining a link. A random geometric graph (RGG) is the main type of synthetic network model used to mimic the statistical properties and behavior of many social networks. We propose a model, called REDS, that extends energy-constrained RGGs to account for the synergic effect of sharing the cost of a link with our neighbors, as is observed in real relational networks. We apply both the standard Watts-Strogatz rewiring procedure and another method that conserves the degree distribution of the network. The second technique was developed to eliminate unwanted forms of spatial correlation between the degree of nodes that are affected by rewiring, limiting the effect on other properties such as clustering and assortativity. We analyze both the statistical properties of these two network types and their epidemiological behavior when used as a substrate for a standard susceptible-infected-susceptible compartmental model. We consider and discuss the differences in properties and behavior between RGGs and REDS as rewiring increases and as infection parameters are changed. We report considerable differences both between the network types and, in the case of REDS, between the two rewiring schemes. We conclude that REDS represent, with the application of these rewiring mechanisms, extremely useful and interesting tools in the study of social and epidemiological phenomena in synthetic complex networks.

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  • Received 7 July 2017

DOI:https://doi.org/10.1103/PhysRevE.96.052316

©2017 American Physical Society

Physics Subject Headings (PhySH)

Networks

Authors & Affiliations

Bryan Iotti1, Alberto Antonioni2,3, Seth Bullock4, Christian Darabos5, Marco Tomassini6, and Mario Giacobini1

  • 1Department of Veterinary Sciences, University of Turin, 10095 Grugliasco, Turin, Italy
  • 2Grupo Interdisciplinar de Sistemas Complejos, Departamento de Matemáticas, Universidad Carlos III de Madrid, E-28911 Leganés, Madrid, Spain
  • 3Institute for Biocomputation and Physics of Complex Systems, University of Zaragoza, E-50018 Zaragoza, Spain
  • 4Department of Computer Science, University of Bristol, BS8 1UB Bristol, England, United Kingdom
  • 5Research Computing, Academic and Campus Technology Services, Dartmouth College, Hanover, New Hampshire 03755, USA
  • 6Information Systems Department, Faculty of Business and Economics, University of Lausanne, CH-1015 Lausanne, Switzerland

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Issue

Vol. 96, Iss. 5 — November 2017

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