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Bursts of vertex activation and epidemics in evolving networks

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Abstract
The dynamic nature of contact patterns creates diverse temporal structures. In particular, empirical studies have shown that contact patterns follow heterogeneous inter-event time intervals, meaning that periods of high activity are followed by long periods of inactivity. To investigate the impact of these heterogeneities in the spread of infection from a theoretical perspective, we propose a stochastic model to generate temporal networks where vertices make instantaneous contacts following heterogeneous inter-event intervals, and may leave and enter the system. We study how these properties affect the prevalence of an infection and estimate R-0, the number of secondary infections of an infectious individual in a completely susceptible population, by modeling simulated infections (SI and SIR) that co-evolve with the network structure. We find that heterogeneous contact patterns cause earlier and larger epidemics in the SIR model in comparison to homogeneous scenarios for a vast range of parameter values, while smaller epidemics may happen in some combinations of parameters. In the case of SI and heterogeneous patterns, the epidemics develop faster in the earlier stages followed by a slowdown in the asymptotic limit. For increasing vertex turnover rates, heterogeneous patterns generally cause higher prevalence in comparison to homogeneous scenarios with the same average inter-event interval. We find that R-0 is generally higher for heterogeneous patterns, except for sufficiently large infection duration and transmission probability.
Keywords
INFECTED-RECOVERED EPIDEMICS, CONTACT NETWORK, HEAVY TAILS, DYNAMICS, DISTRIBUTIONS, MODELS

Citation

Please use this url to cite or link to this publication:

MLA
Rocha, Luis E. C., and Vincent D. Blondel. “Bursts of Vertex Activation and Epidemics in Evolving Networks.” PLOS COMPUTATIONAL BIOLOGY, edited by Marcel Salathé, vol. 9, no. 3, 2013.
APA
Rocha, L. E. C., & Blondel, V. D. (2013). Bursts of vertex activation and epidemics in evolving networks. PLOS COMPUTATIONAL BIOLOGY, 9(3).
Chicago author-date
Rocha, Luis E C, and Vincent D. Blondel. 2013. “Bursts of Vertex Activation and Epidemics in Evolving Networks.” Edited by Marcel Salathé. PLOS COMPUTATIONAL BIOLOGY 9 (3).
Chicago author-date (all authors)
Rocha, Luis E C, and Vincent D. Blondel. 2013. “Bursts of Vertex Activation and Epidemics in Evolving Networks.” Ed by. Marcel Salathé. PLOS COMPUTATIONAL BIOLOGY 9 (3).
Vancouver
1.
Rocha LEC, Blondel VD. Bursts of vertex activation and epidemics in evolving networks. Salathé M, editor. PLOS COMPUTATIONAL BIOLOGY. 2013;9(3).
IEEE
[1]
L. E. C. Rocha and V. D. Blondel, “Bursts of vertex activation and epidemics in evolving networks,” PLOS COMPUTATIONAL BIOLOGY, vol. 9, no. 3, 2013.
@article{8632457,
  abstract     = {The dynamic nature of contact patterns creates diverse temporal structures. In particular, empirical studies have shown that contact patterns follow heterogeneous inter-event time intervals, meaning that periods of high activity are followed by long periods of inactivity. To investigate the impact of these heterogeneities in the spread of infection from a theoretical perspective, we propose a stochastic model to generate temporal networks where vertices make instantaneous contacts following heterogeneous inter-event intervals, and may leave and enter the system. We study how these properties affect the prevalence of an infection and estimate R-0, the number of secondary infections of an infectious individual in a completely susceptible population, by modeling simulated infections (SI and SIR) that co-evolve with the network structure. We find that heterogeneous contact patterns cause earlier and larger epidemics in the SIR model in comparison to homogeneous scenarios for a vast range of parameter values, while smaller epidemics may happen in some combinations of parameters. In the case of SI and heterogeneous patterns, the epidemics develop faster in the earlier stages followed by a slowdown in the asymptotic limit. For increasing vertex turnover rates, heterogeneous patterns generally cause higher prevalence in comparison to homogeneous scenarios with the same average inter-event interval. We find that R-0 is generally higher for heterogeneous patterns, except for sufficiently large infection duration and transmission probability.},
  articleno    = {e1002974},
  author       = {Rocha, Luis E C and Blondel, Vincent D.},
  editor       = {Salathé, Marcel},
  issn         = {1553-7358},
  journal      = {PLOS COMPUTATIONAL BIOLOGY},
  keywords     = {INFECTED-RECOVERED EPIDEMICS,CONTACT NETWORK,HEAVY TAILS,DYNAMICS,DISTRIBUTIONS,MODELS},
  language     = {eng},
  number       = {3},
  title        = {Bursts of vertex activation and epidemics in evolving networks},
  url          = {http://dx.doi.org/10.1371/journal.pcbi.1002974},
  volume       = {9},
  year         = {2013},
}

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