Velocity and hierarchical spread of epidemic outbreaks in scale-free networks.

By Marc Barthelemy, Alain Barrat, Romualdo Pastor-Satorras, Alessandro Vespignani. Physical Review Letters, 2003

648 citations recorded by the source corpus.

We study the effect of the connectivity pattern of complex networks on the propagation dynamics of epidemics. The growth time scale of outbreaks is inversely proportional to the network degree fluctuations, signaling that epidemics spread almost instantaneously in networks with scale-free degree distributions. This feature is associated with an epidemic propagation that follows a precise hierarchical dynamics. Once the highly connected hubs are reached, the infection pervades the network in a progressive cascade across smaller degree classes. The present results are relevant for the development of adaptive containment strategies.

Subfields: Sociology and Political Science, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/dfcf65cfde4848ce8bd19bf174f17ce2f17b8966

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Citations in the corpus

Martingales and fixation probabilities of evolutionary graphs (2014, background): “Outside of evolutionary biology, graph theory or similar concepts have been applied to model economic networks [23], the spread of epidemics in populations [24] and brain connectivity networks [25].”
Modelling dynamical processes in complex socio-technical systems (2011, background): “…of epidemic outbreaks and the growth of the number of infected individuals are governed by a timescale τ proportional to the ratio between the first and second moment of the network’s degree distribution, thus suggesting a velocity of progressionthatincreaseswiththeheterogeneityofthenetwork 52 .”
Dynamical patterns of epidemic outbreaks in complex heterogeneous networks. (2004, positive): “We consider the time behavior of epidemic outbreaks in the general class of models without and with internal recovery and find that the growth of infected individuals is governed by a time-scale t proportional to the ratio between the first and second moment of the network’s degree distribution (Bar”
Critical phenomena in complex networks (2007, background): “, and (49) describe the dynamics of epidemics. 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). The demonstrative SI model is e”
Dynamics and Effective Topology Underlying Synchronization in Networks of Cortical Neurons (2006, positive): “, 2005), dynamic systems coupled in this way display enhanced signal propagation speed that is invariant or even decreases with network size (Strogatz, 2001; Newman, 2003; Barthelemy et al., 2004).”
The fixation probability of a beneficial mutation in a geographically structured population (2011, background): “These new findings have spurred much interest in the field of evolutionary dynamics on graphs[11] and have applications beyond population genetics in domains such as the spread of epidemics[15] or cancer[16, 17] or the appearance of collective behavior[18].”
Discrete-time Markov chain approach to contact-based disease spreading in complex networks (2009, background): “Physicist’s approaches to problems in epidemiology involve statistical physics, the theory of phase transitions and critical phenomena [7], which have been extremely helpful to grasp the macroscopic behavior of epidemic outbreaks [8–16].”
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).”