Oscillatory epidemic prevalence in growing scale-free networks

Hayashi, Yukio; Minoura, Masato; Matsukubo, Jun

doi:10.1103/physreve.69.016112

Cited by 63 publications

(56 citation statements)

References 14 publications

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“…For example, it is found that for a linearly growing network, the evolution of the number of the infected nodes has oscillatory behaviors when the susceptible-infected-recovered (SIR) model is adopted [16]. An adaptive mechanism is studied in [17], where a susceptible individual may avoid the contacts with his infected neighbors and rewire these contacts to other susceptible individuals.…”

Section: Introductionmentioning

confidence: 99%

Epidemic reemergence in adaptive complex networks

et al. 2012

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The dynamic nature of system gives rise to dynamical features of epidemic spreading, such as oscillation and bistability. In this paper, by studying the epidemic spreading in growing networks, in which susceptible nodes may adaptively break the connections with infected ones yet avoid getting isolated, we reveal a new phenomenon -epidemic reemergence, where the number of infected nodes is incubated at a low level for a long time and then bursts up for a short time. The process may repeat several times before the infection finally vanishes. Simulation results show that all the three factors, namely the network growth, the connection breaking and the isolation avoidance, are necessary for epidemic reemergence to happen. We present a simple theoretical analysis to explain the process of reemergence in detail. Our study may offer some useful insights helping explain the phenomenon of repeated epidemic explosions.

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Section: Introductionmentioning

confidence: 99%

Epidemic reemergence in adaptive complex networks

et al. 2012

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“…Both works were analytical, without studying any real graphs. Hayashi et al [2003] study the case of a growing network and derive analytical formulas for such power-law networks (no rewiring). They introduce and study the SHIR model (susceptible, hidden, infectious, recovered), to model computers under email virus attack and derive the conditions for extinction under random and under targeted immunization, always for power-law graphs with no rewiring.…”

Section: Immunizationmentioning

confidence: 99%

Epidemic thresholds in real networks

Chakrabarti

Wang

et al. 2008

ACM Trans. Inf. Syst. Secur.

666

689

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How will a virus propagate in a real network? How long does it take to disinfect a network given particular values of infection rate and virus death rate? What is the single best node to immunize? Answering these questions is essential for devising network-wide strategies to counter viruses. In addition, viral propagation is very similar in principle to the spread of rumors, information, and "fads," implying that the solutions for viral propagation would also offer insights into these other problem settings. We answer these questions by developing a nonlinear dynamical system (NLDS) that accurately models viral propagation in any arbitrary network, including real and synthesized network graphs. We propose a general epidemic threshold condition for the NLDS system: we prove that the epidemic threshold for a network is exactly the inverse of the largest eigenvalue of its adjacency matrix. Finally, we show that below the epidemic threshold, infections die out at an exponential rate. Our epidemic threshold model subsumes many known thresholds for special-case graphs (e.g., Erdös-Rényi, BA powerlaw, homogeneous). We demonstrate the predictive power of our model with extensive experiments on real and synthesized graphs, and show that our threshold condition holds for arbitrary graphs. Finally, we show how to utilize our threshold condition for practical uses: It can dictate which nodes to immunize; it can assess the effects of a throttling policy; it can help us design network topologies so that they are more resistant to viruses.

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“…Not only their topological features, but also their dynamical properties have been clarified. For example, it has been revealed that the scale-free structure has large influence on dynamics in its heterogeneous structure [5,6,7]. It has been shown that the epidemic threshold vanishes if their degree distributions have a power-law form, P (k) ∼ k −γ , where the characteristic degree exponent γ is lower than 3 [5].…”

Section: Introductionmentioning

confidence: 99%

Statistical-mechanical iterative algorithms on complex networks

2005

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The Ising models have been applied for various problems on information sciences, social sciences, and so on. In many cases, solving these problems corresponds to minimizing the Bethe free energy. To minimize the Bethe free energy, a statistical-mechanical iterative algorithm is often used. We study the statistical-mechanical iterative algorithm on complex networks. To investigate effects of heterogeneous structures on the iterative algorithm, we introduce an iterative algorithm based on information of heterogeneity of complex networks, in which higher-degree nodes are likely to be updated more frequently than lower-degree ones. Numerical experiments clarified that the usage of the information of heterogeneity affects the algorithm in Barabási and Albert networks, but does not influence that in Erdös and Rényi networks. It is revealed that information of the whole system propagates rapidly through such high-degree nodes in the case of Barabási-Albert's scale-free networks.

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Oscillatory epidemic prevalence in growing scale-free networks

Cited by 63 publications

References 14 publications

Epidemic reemergence in adaptive complex networks

Epidemic reemergence in adaptive complex networks

Epidemic thresholds in real networks

Statistical-mechanical iterative algorithms on complex networks

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