Epidemic threshold and control in a dynamic network

Michael Taylor, Timothy J. Taylor, and Istvan Z. Kiss
Phys. Rev. E 85, 016103 – Published 5 January 2012

Abstract

In this paper we present a model describing susceptible-infected-susceptible-type epidemics spreading on a dynamic contact network with random link activation and deletion where link activation can be locally constrained. We use and adapt an improved effective degree compartmental modeling framework recently proposed by Lindquist et al. [J. Math Biol. 62, 143 (2010)] and Marceau et al. [Phys. Rev. E 82, 036116 (2010)]. The resulting set of ordinary differential equations (ODEs) is solved numerically, and results are compared to those obtained using individual-based stochastic network simulation. We show that the ODEs display excellent agreement with simulation for the evolution of both the disease and the network and are able to accurately capture the epidemic threshold for a wide range of parameters. We also present an analytical R0 calculation for the dynamic network model and show that, depending on the relative time scales of the network evolution and disease transmission, two limiting cases are recovered: (i) the static network case when network evolution is slow and (ii) homogeneous random mixing when the network evolution is rapid. We also use our threshold calculation to highlight the dangers of relying on local stability analysis when predicting epidemic outbreaks on evolving networks.

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  • Received 2 June 2011

DOI:https://doi.org/10.1103/PhysRevE.85.016103

©2012 American Physical Society

Authors & Affiliations

Michael Taylor1,*, Timothy J. Taylor1,2, and Istvan Z. Kiss1

  • 1School of Mathematical and Physical Sciences, Department of Mathematics, University of Sussex, Brighton UK-BN1 9QH, England, United Kingdom
  • 2Centre for Computational Neuroscience and Robotics, University of Sussex, Brighton UK-BN1 9QH, England, United Kingdom

  • *mt264@sussex.ac.uk

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Vol. 85, Iss. 1 — January 2012

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