Networks and the Epidemiology of Infectious Disease

Danon, León; Ford, Ashley; House, Thomas; Jewell, Chris; Keeling, Matthew James; Roberts, Gareth O.; Ross, Joshua V.; Vernon, Matthew C.

doi:10.1155/2011/284909

Cited by 375 publications

(337 citation statements)

References 184 publications

(280 reference statements)

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“…They appear in numerous complex systems including in nanoscience [3], epidemiology [4,5], forest fires [6], social networks [7,8], and wireless communications [9][10][11]. Such networks exhibit a general phenomenon called percolation [12,13], where at a critical connection probability (controlled by the node density), the largest connected component (cluster) of the network jumps abruptly from being independent of system size (microscopic) to being proportional to system size (macroscopic).…”

Section: Introductionmentioning

confidence: 99%

Impact of boundaries on fully connected random geometric networks

2012

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Many complex networks exhibit a percolation transition involving a macroscopic connected component, with universal features largely independent of the microscopic model and the macroscopic domain geometry. In contrast, we show that the transition to full connectivity is strongly influenced by details of the boundary, but observe an alternative form of universality. Our approach correctly distinguishes connectivity properties of networks in domains with equal bulk contributions. It also facilitates system design to promote or avoid full connectivity for diverse geometries in arbitrary dimension.

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Section: Introductionmentioning

confidence: 99%

Impact of boundaries on fully connected random geometric networks

2012

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“…Without prejudice to the generality of Section 2, we now focus our study to spreading processes [15,16,17]. An epidemiological terminology is used: whatever propagates among neighbouring nodes, be it desirable or not, is called an infection.…”

Section: Application To Spreading Dynamicsmentioning

confidence: 99%

Spreading dynamics on complex networks: a general stochastic approach

et al. 2013

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Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our systematic framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agentbased computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible (SIS) and susceptible-infectious-removed (SIR) dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.

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“…It is conceivable that rumor/disease transmission and virus/worm transmission are easily understood in a social network and computer network, respectively, if we understand the network well. In general, it is recognized that epidemic threshold in a network is given by the basic reproduction ratio [22], but it is also related to the largest eigen value of the adjacency matrix of the network [23], to be exact it is reciprocal. This has motivated us to explore the relation between cliques of a graph and the eigen values of the adjacency matrix of the graph.…”

Section: Introductionmentioning

confidence: 99%

A review on eigen values of adjacency matrix of graph with cliques

Carnia¹,

Suyudi²,

Aisah³

et al. 2017

AIP Conference Proceedings

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Abstract.The paper reviews the applications of eigen value in different areas. One of the area is in the analysis of graphs coming from networks. The development of theory regarding the eigenvalues and its maximum eigenvalue of the adjacency matrix arising from a general graph is already well-established. Here we review some notions from different context, i.e. led by observation of some simple experiments regarding the relation between graph, cliques, and the eigen values of the adjacency matrix. We focus on regular graphs having one or more cliques in their graph structures. We do some numerical experiment on the computation of the eigen values of the adjacency matrix and show some patterns on the relation between the structure of the graph (e.g. the maximum cliques, chromatic number) and the eigen values of the adjacency matrix. By observing these patterns we find some conclusion, such as: i. the maximum clique of a complete graph is given by the largest eigen value plus one; ii. the maximum clique of a cycle graph (simple incomplete regular graph) equals the largest eigen value, in which the value is two; iii. the maximum multiplicity of the eigen values of a cycle graph is two. Future direction of the development is also presented based on the careful analysis of the existing development.

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Networks and the Epidemiology of Infectious Disease

Cited by 375 publications

References 184 publications

Impact of boundaries on fully connected random geometric networks

Impact of boundaries on fully connected random geometric networks

Spreading dynamics on complex networks: a general stochastic approach

A review on eigen values of adjacency matrix of graph with cliques

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