Dynamical patterns of epidemic outbreaks in complex heterogeneous networks.

By Marc Bartheíemy, Alain Barrat, Romualdo Pastor-Satorras, Alessandro Vespignani. Journal of Theoretical Biology, 2004

531 citations recorded by the source corpus.

We present a thorough inspection of the dynamical behavior of epidemic phenomena in populations with complex and heterogeneous connectivity patterns. We show that the growth of the epidemic prevalence is virtually instantaneous in all networks characterized by diverging degree fluctuations, independently of the structure of the connectivity correlation functions characterizing the population network. By means of analytical and numerical results, we show that the outbreak time evolution follows a precise hierarchical dynamics. Once reached the most highly connected hubs, the infection pervades the network in a progressive cascade across smaller degree classes. Finally, we show the influence of the initial conditions and the relevance of statistical results in single case studies concerning heterogeneous networks. The emerging theoretical framework appears of general interest in view of the recently observed abundance of natural networks with complex topological features and might provide useful insights for the development of adaptive strategies aimed at epidemic containment.

Subfields: Sociology and Political Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c8d52c08764901d9bbfab7951b3f8eb52cfe40ab

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Citations in the corpus

Graph theory and networks in Biology. (2006, result): “These findings are in agreement with those described in [241], which indicate that disease spreads in a hierarchical cascade from hub nodes to nodes with intermediate degree to nodes with low degree.”
Epidemic modeling in metapopulation systems with heterogeneous coupling pattern: theory and simulations. (2007, background): “Finally, it is interesting to notice that the effect of the network heterogeneity on the subpopulation reproductive number is similar to that of the contact pattern heterogeneity on the basic reproductive number (Anderson and May, 1992; Pastor-Satorras and Vespignani, 2001a; Lloyd and May, 2001; Bar”
Large graph limit for an SIR process in random network with heterogeneous connectivity (2010, unknown): “Mean ﬁeld approximations ( e.g. [23, 4, 10]) or large population approximations ( e.g. [3], see also Eq.”
Knowledge transfer in a tourism destination: the effects of a network structure (2009, methodology): “Despite its simplicity, this class of model has been shown to be quite effective and to be a good approximation of more refined and complex models (Barthélemy et al., 2005; Xu et al., 2007).”
When individual behaviour matters: homogeneous and network models in epidemiology (2007, background): “The structures of human contact networks undoubtedly play a crucial role in the transmission of diseases (Pastor-Satorras & Vespignani 2001; Newman 2002; Barthélemy et al. 2004, 2005; Meyers et al. 2005; Ferrari et al. 2006).”
Structure of the social network and its influence on transmission dynamics in a honeybee colony (2008, background): “The interest in this emerging area has however come mostly from epidemiology (Read and Keeling 2003; Barthélemy et al. 2005; Keeling 2005; Saramäki and Kaski 2005; Verdasca et al. 2005) and community ecology (Dunne et al.”
Critical phenomena in complex networks (2007, background): “Let us discuss this dynamics above an epidemic threshold, where epidemic outbreaks are giant, that is involve a finite fraction of vertices in a network (Barthelemy et al., 2004, 2005; Moreno et al., 2002; Vazquez, 2006a).”
Universality in network dynamics (2013, unknown): “To be sure, advances in our understanding of synchronization [17, 18], spreading processes [19–21] or spectral phenomena [22] have offered important clues on the interplay between network topology and network dynamics.”