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Chaos / Volume 22 / Issue 1 / REGULAR ARTICLES
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Chaos 22, 013101 (2012); http://dx.doi.org/10.1063/1.3673573 (8 pages)

The impact of awareness on epidemic spreading in networks

Qingchu Wu1, Xinchu Fu2,3, Michael Small4,5, and Xin-Jian Xu2,3

1College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China
2Department of Mathematics, Shanghai University, Shanghai 200444, China
3Institute of Systems Science, Shanghai University, Shanghai 200444, China
4School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia
5Department of Electronic and Information Engineering, Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

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(Received 29 March 2011; accepted 9 December 2011; published online 3 January 2012)

We explore the impact of awareness on epidemic spreading through a population represented by a scale-free network. Using a network mean-field approach, a mathematical model for epidemic spreading with awareness reactions is proposed and analyzed. We focus on the role of three forms of awareness including local, global, and contact awareness. By theoretical analysis and simulation, we show that the global awareness cannot decrease the likelihood of an epidemic outbreak while both the local awareness and the contact awareness can. Also, the influence degree of the local awareness on disease dynamics is closely related with the contact awareness.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THE MODEL
  3. EPIDEMIC THRESHOLD
  4. SIMULATIONS
  5. CONCLUSIONS AND DISCUSSIONS

RELATED DATABASES

Web of Science

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KEYWORDS and PACS

Keywords

complex networks, diseases, epidemics, nonlinear dynamical systems

PACS

  • 05.45.-a

    Nonlinear dynamics and chaos

  • 87.23.Cc

    Population dynamics and ecological pattern formation

  • 89.75.-k

    Complex systems

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3673573

PUBLICATION DATA

ISSN

1054-1500 (print)  
1089-7682 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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Figures (click on thumbnails to view enlargements)

FIG.1
(Color online) The degree distribution of a BA scale-free network used in our simulations. This plot shows that P(k) ∼ k−3.

FIG.1 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.2
(Color online) Plot of λc versus α and β with ψ(k) = k−0.3. When considering λc versus α, we set β = 0.3; when considering λc versus β, we set α = 0.6. “SS” means stochastic simulations and “MF” means mean-field predictions. All stochastic simulations are performed on the same BA scale-free networks and mean-field predictions are obtained by numerically integrating the ordinary differential Eq. ( 9 ), where the degree distribution P(k) is obtained from the stochastic simulation.

FIG.2 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.3
(Color online) Plot of λc versus α and β with ψ(k) = k−0.8. When considering λc versus α, we set β = 0.3; when considering λc versus β, we set α = 0.6. All the simulations are performed on the same BA scale-free networks as illustrated in Fig. 2.

FIG.3 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.4
(Color online) Plot of λc versus b. We use parameters α = 0.6 and β = 0.3. All the simulations are performed on the same BA scale-free networks as illustrated in Fig. 2.

FIG.4 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.5
(Color online) The effect of parameter α and β on the final epidemic size ρ for λ = 0.2 and λ = 0.4 under b = 0. All the simulations are performed on the same BA scale-free networks.

FIG.5 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.6
(Color online) The variation of ΔF with respect to α and β. Parameters: ɛ = 0.01, λ = 0.2 and b = 0.

FIG.6 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.7
(Color online) Comparison of a mean-field prediction Eq. ( 9 ) and the average of 1000 runs of stochastic simulations for the SIS model on the same BA scale-free network with α = 0.6, β = 0.3, λ= 0.05, γ = 0.1, b = 0, N = 10 000, 〈k〉 = 6. In stochastic simulations, we take h = 0.1, h = 0.5, and h = 1, respectively. This plot displays different time ranges: (a) t ∈ [0,1000]; (b) t ∈ [0,50]; (c) t ∈ [950,1000].

FIG.7 Download High Resolution Image (.zip file) | Export Figure to PowerPoint

FIG.8
(Color online) The plot of the local infection density at the steady state ρknm(∞) with respect to k. Parameters: λ = 0.1, b = 0, α = 0.6, and β = 0.3.

FIG.8 Download High Resolution Image (.zip file) | Export Figure to PowerPoint



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