Percolation and epidemics in random clustered networks

Miller, Joel C.

doi:10.1103/physreve.80.020901

Cited by 257 publications

(383 citation statements)

References 20 publications

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“…In particular, we assume that clustering [47,48] is negligible: partners are unlikely to see one another. This assumption applies equally to most existing analytical epidemic models, but it can be eliminated in very special cases using techniques similar to those of earlier studies [49][50][51][52]. …”

Section: Discussionmentioning

confidence: 99%

Edge-based compartmental modelling for infectious disease spread

Miller

Slim²,

Volz

2011

J. R. Soc. Interface.

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231

302

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The primary tool for predicting infectious disease spread and intervention effectiveness is the mass action susceptible -infected -recovered model of Kermack & McKendrick. Its usefulness derives largely from its conceptual and mathematical simplicity; however, it incorrectly assumes that all individuals have the same contact rate and partnerships are fleeting. In this study, we introduce edge-based compartmental modelling, a technique eliminating these assumptions. We derive simple ordinary differential equation models capturing social heterogeneity (heterogeneous contact rates) while explicitly considering the impact of partnership duration. We introduce a graphical interpretation allowing for easy derivation and communication of the model and focus on applying the technique under different assumptions about how contact rates are distributed and how long partnerships last.

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Section: Discussionmentioning

confidence: 99%

Edge-based compartmental modelling for infectious disease spread

Miller

Slim²,

Volz

2011

J. R. Soc. Interface.

Self Cite

231

302

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show abstract

“…This example exhibits different results for theory and numerics even in the Facebook networks. This suggests that the σ = 0 case of the Watts model is particularly sensitive to deviations of the network from randomness and suggests that this case might provide a suitable testing ground for new analytically tractable models of networks that include clustering [13,14,22].…”

Section: Discussionmentioning

confidence: 99%

“…Furthermore, if one considers a dynamical system on a real-world network rather than on a grossly simplified caricature of it, then theoretical results become almost barren. This has motivated a wealth of recent research concerning analytical results on networks with clustering [7,[11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

The unreasonable effectiveness of tree-based theory for networks with clustering

et al. 2011

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We demonstrate that a tree-based theory for various dynamical processes operating on static, undirected networks yields extremely accurate results for several networks with high levels of clustering. We find that such a theory works well as long as the mean intervertex distance is sufficiently small-that is, as long as it is close to the value of in a random network with negligible clustering and the same degree-degree correlations. We support this hypothesis numerically using both real-world networks from various domains and several classes of synthetic clustered networks. We present analytical calculations that further support our claim that tree-based theories can be accurate for clustered networks, provided that the networks are "sufficiently small" worlds.

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“…Cascades in social networks like these may require networks with triangles or other subgraphs added (53,64,65); inverting the resulting multidimensional generating function equations for dynamics on these networks would require similar multitype techniques as developed here.…”

Section: Applied Mathematics Pnas Plusmentioning

confidence: 99%

Suppressing cascades of load in interdependent networks

Brummitt¹,

D’Souza

Leicht

2012

Proc. Natl. Acad. Sci. U.S.A.

491

347

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Understanding how interdependence among systems affects cascading behaviors is increasingly important across many fields of science and engineering. Inspired by cascades of load shedding in coupled electric grids and other infrastructure, we study the BakTang-Wiesenfeld sandpile model on modular random graphs and on graphs based on actual, interdependent power grids. Starting from two isolated networks, adding some connectivity between them is beneficial, for it suppresses the largest cascades in each system. Too much interconnectivity, however, becomes detrimental for two reasons. First, interconnections open pathways for neighboring networks to inflict large cascades. Second, as in real infrastructure, new interconnections increase capacity and total possible load, which fuels even larger cascades. Using a multitype branching process and simulations we show these effects and estimate the optimal level of interconnectivity that balances their trade-offs. Such equilibria could allow, for example, power grid owners to minimize the largest cascades in their grid. We also show that asymmetric capacity among interdependent networks affects the optimal connectivity that each prefers and may lead to an arms race for greater capacity. Our multitype branching process framework provides building blocks for better prediction of cascading processes on modular random graphs and on multitype networks in general.vulnerability of infrastructure | complex networks

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Percolation and epidemics in random clustered networks

Cited by 257 publications

References 20 publications

Edge-based compartmental modelling for infectious disease spread

Edge-based compartmental modelling for infectious disease spread

The unreasonable effectiveness of tree-based theory for networks with clustering

Suppressing cascades of load in interdependent networks

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