Epidemic dynamics in finite size scale-free networks.

By Romualdo Pastor-Satorras, Alessandro Vespignani. Physical review. E, Statistical, nonlinear, and soft matter physics, 2002

685 citations recorded by the source corpus.

Many real networks present a bounded scale-free behavior with a connectivity cutoff due to physical constraints or a finite network size. We study epidemic dynamics in bounded scale-free networks with soft and hard connectivity cutoffs. The finite size effects introduced by the cutoff induce an epidemic threshold that approaches zero at increasing sizes. The induced epidemic threshold is very small even at a relatively small cutoff, showing that the neglection of connectivity fluctuations in bounded scale-free networks leads to a strong overestimation of the epidemic threshold. We provide the expression for the infection prevalence and discuss its finite size corrections. The present paper shows that the highly heterogeneous nature of scale-free networks does not allow the use of homogeneous approximations even for systems of a relatively small number of nodes.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1fd3dc5d50f2b643b2d48fa9b3c2991cda5998bf

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Citations in the corpus

Evolution and Structure of the Internet: Index (2004, methodology): “Focusing in the SIS model in uncorrelated random networks with a scale-free degree distribution of the form P(k) k−γ exp(−k/kc), we can compute the effective non-zero epidemic threshold λc(kc) within the continuous k approximation (Pastor-Satorras and Vespignani, 2002)”
Modelling dynamical processes in complex socio-technical systems (2011, background): “Although this is not the case in any finite-size real-world network 50,51 , larger heterogeneity levels lead to smaller epidemic thresholds (Fig.”
Random Graph Dynamics: References (2006, background): “, Preston (1974). NW small world, k = 1.”
The Structure and Function of Complex Networks (2003, background): “They have also generalized the solution to a number of other cases, including other degree distributions [332], finite-sized networks [334], and models that include vaccination of some fraction of individuals [335, 336].”
Simulated Epidemics in an Empirical Spatiotemporal Network of 50,185 Sexual Contacts (2010, background): “is the number of different partners of an individual”
The effect of network topology on the spread of epidemics (2005, methodology): “For example, [ 16 ] uses a mean field approximation for establishing conditions for quick and slow die out in scale-free graphs and [12] provides an approximate analysis for the case of an Erd ý os-Renyi graph.”
Epidemics and immunization in scale‐free networks (2002, methodology): “Explicit calculatio ns can be performed for the SIS model [ 39 ] in SF networks with exponentially bounded connectivity, P(k) ∼ k exp(−k/kc), obtaining that the effective nonzero epidemic threshold �c(kc) induced by the cut-off kc behaves as”
When individual behaviour matters: homogeneous and network models in epidemiology (2007, background): “Moreno et al. (2002) and Pastor-Satorras & Vespignani (2002) have developed a dynamical framework based on”
Global Stability of Infectious Disease Models Using Lyapunov Functions (2013, neutral): “with the mean-field reaction rate equations of the SIS disease model proposed by Pastor-Satorras and Vespignani for epidemic spreading in scale-free networks [29, 30].”
The impacts of network topology on disease spread (2005, background): “The nature of epidemiological spread in scale-free networks is known to be dramatically different from other networks because of this high level of global heterogeneity (Pastor-Satorras and Vespignani, 2002; Rhodes and Anderson, 1996).”
Graph theory and networks in Biology. (2006, background): “Finite-size effects have also been discussed in this context [217, 218].”