Nonequilibrium phase transitions and finite size scaling in weighted scale-free networks (original) (raw)
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We use scale-free networks to study properties of the infected mass M of the network during a spreading process as a function of the infection probability q and the structural scaling exponent . We use the standard SIR model and investigate in detail the distribution of M . We ÿnd that for dense networks this function is bimodal, while for sparse networks it is a smoothly decreasing function, with the distinction between the two being a function of q. We thus recover the full crossover transition from one case to the other. This has a result that on the same network, a disease may die out immediately or persist for a considerable time, depending on the initial point where it was originated. Thus, we show that the disease evolution is signiÿcantly in uenced by the structure of the underlying population.
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We numerically investigate the existence of a threshold for epidemic outbreaks in a class of scale-free networks characterized by a parametrical dependence of the scaling exponent, influencing the convergence of fluctuations in the degree distribution. In finite-size networks, finite thresholds for the spreading of an epidemic are always found. However, both the thresholds and the behavior of the epidemic prevalence are quite different with respect to the type of network considered and the system size. We also discuss agreements and differences with some analytical claims previously reported.
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Physica A-statistical Mechanics and Its Applications, 2007
We study geographical effects on the spread of diseases in lattice-embedded scalefree networks. The geographical structure is represented by the connecting probability of two nodes that is related to the Euclidean distance between them in the lattice. By studying the standard Susceptible-Infected model, we found that the geographical structure has great influences on the temporal behavior of epidemic outbreaks and the propagation in the underlying network: the more geographically constrained the network is, the more smoothly the epidemic spreads, which is different from the clearly hierarchical dynamics that the infection pervades the networks in a progressive cascade across smaller-degree classes in Barabási-Albert scale-free networks.
2014
The epidemic threshold of the susceptible-infected-susceptible (SIS) dynamics on random networks having a power law degree distribution with exponent gamma>3\gamma>3gamma>3 has been investigated using different mean-field approaches, which predict different outcomes. We performed extensive simulations in the quasistationary state for a comparison with these mean-field theories. We observed concomitant multiple transitions in individual networks presenting large gaps in the degree distribution and the obtained multiple epidemic thresholds are well described by different mean-field theories. We observed that the transitions involving thresholds which vanishes at the thermodynamic limit involve localized states, in which a vanishing fraction of the network effectively contribute to epidemic activity, whereas an endemic state, with a finite density of infected vertices, occurs at a finite threshold. The multiple transitions are related to the activations of distinct sub-domains of the network, which are not directly connected.
Infection Dynamics on Scale-Free Networks
Physical Review E, 2001
Infection dynamics on scale-free networks. Robert M. May 1 and Alun L. Lloyd 2 * 1 Department of Zoology, University of Oxford, South Parks Road, Oxford OX1 3PS, United Kingdom 2 Program in Theoretical Biology, Institute for Advanced Study, Princeton, New Jersey 08540. ...
Transactions of The Society for Modeling and Simulation International, 2009
In a recent paper entitled 'Influences of Resource Limitations and Transmission Costs on Epidemic Simulations and Critical Thresholds in Scale-Free Networks' by Huang et al., the authors attempted to establish a key characteristic of epidemic dynamics in a scale-free network when properly accounting for the cost of transmitting the infection at each node and the resources available for transmission to that node. The main input parameter is the effective rate of spreading the infection, i.e. the instantaneous rate at which the infection is spread to an uninfected node via a single link to an infected node. The primary result is the existence of a positive critical threshold for the infection-spreading rate at or below which the epidemic dies out and above which the epidemic is spread through the network and ultimately reaches a steady-state non-vanishing condition. Some flaws in the authors' proof of this result are discussed, and an alternative derivation is provided that sheds additional light on the transient and steady-state behavior of the system. The alternative derivation may be adapted to the analysis of other scale-free networks with different features.
A stochastic SIR epidemic on scale-free network with community structure
The scale-free degree distribution and community structure are two significant properties shared by numerous complex networks. In this paper, we investigate the impact of these properties on a stochastic SIR epidemic which incorporates the stochastic nature of epidemic spreading. A two-type branching process is employed to approximate the early stage of epidemic spreading. The basic reproduction number R0 is obtained. And the influences of scale-free property and community structure on R0 are analyzed by numerical simulations.