Networks and epidemic models.
Citations
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7,116 citations
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Cites background from "Networks and epidemic models."
...…different disciplines, and in the last ten years an impressive array of methods and approaches ranging from mean-field theories to rigorous results have provided new quantitative insights on the dynamics of contagion processes in complex networks (Danon et al., 2011; Keeling and Eames, 2005)....
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1,476 citations
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Cites methods from "Networks and epidemic models."
...One canonical model used as a candidate for network equivalence is the original Watts-Strogatz (WS) model, which has been used as a substrate for studying dynamics in the diverse fields of ecology [8], economics [9,10], epidemiology [11,12], and neuroscience [13]....
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973 citations
Cites background from "Networks and epidemic models."
...This nonrandom mixing can in theory be described through the use of network models that include more detail information about who mixes with whom [26]....
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References
39,297 citations
"Networks and epidemic models." refers background in this paper
...The high level of clustering means that most infection occurs locally, but short path lengths mean that epidemic spread through the network is rapid and disease is unlikely to be contained within small regions of the population ( Watts & Strogatz 1998 )....
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...Small-world networks, described in the work of Watts & Strogatz (1998; see also Watts 1999), offer a means of moving between the rigid arrangement of lattices and the unstructured connections of random networks....
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...While collecting network data is beset with difficulties, the simulation of disease transmission on networks is relatively straightforward (Eames & Keeling 2002; Eubank et al. 2004; Meyers et al. 2005; Read & Keeling 2003; Wallinga et al. 1999; Watts & Strogatz 1998 ), relying on the observation that...
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...…mixing networks, the concepts underlying percolation theory are immediately relevant to epidemiology, and many of these ideas and the tools for understanding them have been applied in epidemiological settings (Mollison 1977; Grassberger 1983; Newman & Watts 1999; Newman 2002; Warren et al. 2002)....
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...On a much smaller scale are gene and neural networks, which display the high clustering and low path lengths associated with the small-world model ( Watts & Strogatz 1998 )....
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33,771 citations
"Networks and epidemic models." refers background in this paper
...In many observed networks, this is far from homogeneous; it is often the case that many individuals have a small number of neighbours, while a few have significantly more connections (Albert et al. 1999; Barabási & Albert 1999; Jeong et al. 2000; Liljeros et al. 2001)....
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...Scale-free networks can be constructed dynamically by adding new individuals to a network one by one with a connection mechanism that mimics the natural formation of social contacts (Barabási & Albert 1999;Albert et al. 2000; Pastor-Satorras & Vespignani 2001)....
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...This property was initially observed for worldwide Web connections (Albert et al. 1999), but has also been reported in power grid networks, graphs of actor collaborations (Barabási & Albert 1999) and networks of human sexual contacts (Liljeros et al. 2001)....
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...In the preferential attachment model of Barabási & Albert (1999), the existence of individuals of arbitrarily large degree means that there is no level of random vaccination that is sufficient to prevent an epidemic (Albert et al. 2000; Lloyd&May 2001; Pastor-Satorras& Vespignani 2001)....
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17,104 citations
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16,023 citations
"Networks and epidemic models." refers background or methods in this paper
...In this case, the network of relevant interactions would be a directed graph (Harary 1969; Bollobás 1979)....
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...I N Z b I N : ð1:3Þ This leads to a nonlinear term (bSI/N ) representing the transmission of infection, generating a variety of rich dynamical behaviours (Schwartz 1985; Olsen et al. 1986; Rand & Wilson 1991; Anderson & May 1992; Earn et al. 2000; Keeling et al. 2001)....
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...We can use an ‘adjacency matrix’ or ‘sociomatrix’, A, to describe the connections within a population (Harary 1969; Bollobás 1979; Wasserman & Faust 1994; West 1996); AijZ1 if there is a connection such that infection could pass from individual i to individual j ; otherwise, AijZ0....
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8,238 citations