Epidemic Spreading in Scale-Free Networks

Pastor-Satorras, Romualdo; Vespignani, Alessandro

doi:10.1103/physrevlett.86.3200

Cited by 5,102 publications

(3,720 citation statements)

References 16 publications

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“…So the epidemic threshold is determined by three parameters(N, β, γ) and the networks degree distribution p(k). We notice that the expression (23) involves multiplication of the well-known term k k 2 [2,4,6,9], which is closely related to the "average" number of secondary infections [7,8]. Not surprising, this result is the same as that of the standard SIS model [4].…”

Section: N>2supporting

confidence: 73%

“…It is worth noticing that N i=0 u k,i = 1. According to the transitions rate described in the above section, the evolution equations of u k,i are written as below [4,6]:…”

Section: Mean-field Equationsmentioning

confidence: 99%

“…If the effective spreading rate λ>λ c , the infection spreads and becomes endemic; otherwise the infection will die out. While the threshold disappears on scale-free networks [4].…”

Section: Introductionmentioning

confidence: 99%

“…The dynamical behavior of so-called susceptibleinfected-susceptible (SIS) model and susceptible-infected-removed (SIR) model have been widely investigated on regular network and complex networks [1][2][3][4][5][6][7][8][9][10][11][12]. Within the studying, individuals are modeled as sites and possible contacts between individuals are linked by edges between the sites.…”

Section: Introductionmentioning

confidence: 99%

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The spread of infectious disease on complex networks with household-structure

Liu

Yang

2004

Physica A: Statistical Mechanics and its Applications

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In this paper we study the household-structure SIS epidemic spreading on general complex networks. The household structure gives us the way to distinguish inner and the outer infection rate. Unlike household-structure models on homogenous networks, such as regular and random networks, here we consider heterogeneous networks with arbitrary degree distribution p(k). First we introduce the epidemic model. Then rate equations under mean field appropriation and computer simulations are used here to analyze our model. Some unique phenomena only existing in divergent network with household structure is found, while we also get some similar conclusions that some simple geometrical quantities of networks have important impression on infection property of infectous disease. It seems that in our model even when local cure rate is greater than inner infection rate in every household, disease still can spread on scale-free network. It implies that no disease is spreading in every single household, but for the whole network, disease is spreading. Since our society network seems like this structure, maybe this conclusion remind us that during disease spreading we should pay more attention on network structure than local cure condition.

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Section: N>2supporting

confidence: 73%

“…It is worth noticing that N i=0 u k,i = 1. According to the transitions rate described in the above section, the evolution equations of u k,i are written as below [4,6]:…”

Section: Mean-field Equationsmentioning

confidence: 99%

“…If the effective spreading rate λ>λ c , the infection spreads and becomes endemic; otherwise the infection will die out. While the threshold disappears on scale-free networks [4].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The spread of infectious disease on complex networks with household-structure

Liu

Yang

2004

Physica A: Statistical Mechanics and its Applications

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“…Thus one would expect that epidemic models on graphs are relevant to the study of information flow in organizations. In particular, recent work on epidemic propagation on scale free networks found that the threshold for an epidemic is zero, implying that a finite fraction of the graph becomes infected for arbitrarily low transmission probabilities [6,7,8]. The presence of additional network structure was found to further influence the spread of disease on scale-free graphs [9, 10, 11].…”

mentioning

confidence: 99%

Information flow in social groups

Huberman

Adamic

et al. 2004

Physica A: Statistical Mechanics and its Applications

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141

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We present a study of information flow that takes into account the observation that an item relevant to one person is more likely to be of interest to individuals in the same social circle than those outside of it. This is due to the fact that the similarity of node attributes in social networks decreases as a function of the graph distance. An epidemic model on a scale-free network with this property has a finite threshold, implying that the spread of information is limited. We tested our predictions by measuring the spread of messages in an organization and also by numerical experiments that take into consideration the organizational distance among individuals.The problem of information flows in social organizations is relevant to issues of productivity, innovation and the sorting out of useful ideas out of the general chatter of a community. How information spreads determines the speed with which individuals can act and plan their future activities. In particular, email has become the predominant means of communication in the information society. It pervades business, social and scientific exchanges and as such it is a highly relevant area for research on communities and social networks. Not surprisingly, email has been established as an indicator of collaboration and knowledge exchange [1,2,3,4,5]. Email is also a good medium for research because it provides plentiful data on personal communication in an electronic form.Since individuals tend to organize both formally and informally into groups based on their common activities and interests, the way information spreads is affected by the topology of the interaction network, not unlike the spread of a disease among individuals. Thus one would expect that epidemic models on graphs are relevant to the study of information flow in organizations. In particular, recent work on epidemic propagation on scale free networks found that the threshold for an epidemic is zero, implying that a finite fraction of the graph becomes infected for arbitrarily low transmission probabilities [6,7,8]. The presence of additional network structure was found to further influence the spread of disease on scale-free graphs [9, 10, 11].There are, however, differences between information flows and the spread of viruses. While viruses tend to be indiscriminate, infecting any susceptible individual, information is selective and passed by its host only to individuals the host thinks would be interested in it.The information any individual is interested in depends strongly on their characteristics. Furthermore, individuals with similar characteristics tend to associate with one another, a phenomenon known as homophily [12,13,14]. Conversely, individuals many steps removed in a social network on average tend not to have as much in common, as shown in a study [15] of a network of Stanford student homepages and illustrated in Figure 1.We therefore introduce an epidemic model with decay in the transmission probability of a particular piece of in- formation as a function of the distance between t...

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Wavelet correlations to reveal multiscale coupling in geophysical systems

et al. 2015

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The interactions between climate and the environment are highly complex. Due to this complexity, process-based models are often preferred to estimate the net magnitude and directionality of interactions in the Earth system. However, these models are based on simplifications of our understanding of nature and thus are unavoidably imperfect. Conversely, observation-based data of climatic and environmental variables are becoming increasingly accessible over global scales due to the progress of spaceborne sensing technologies and data-assimilation techniques. Albeit uncertain, these data enable the possibility to start unraveling complex multivariable, multiscale relationships if the appropriate statistical methods are applied. Here we investigate the potential of the wavelet cross-correlation method as a tool for identifying time/frequency-dependent interactions, feedback, and regime shifts in geophysical systems. The ability of wavelet cross-correlation to resolve the fast and slow components of coupled systems is tested on synthetic data of known directionality and then applied to observations to study one of the most critical interactions between land and atmosphere: the coupling between soil moisture and near-ground air temperature. Results show that our method is able to capture the dynamics of the soil moisture-temperature coupling over a wide range of temporal scales (from days to several months) and climatic regimes (from wet to dry) and consistently identify the magnitude and directionality of the coupling. Consequently, wavelet cross-correlations are presented as a promising tool for the study of multiscale interactions, with the potential of being extended to the analysis of causal relationships in the Earth system

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Epidemic Spreading in Scale-Free Networks

Cited by 5,102 publications

References 16 publications

The spread of infectious disease on complex networks with household-structure

The spread of infectious disease on complex networks with household-structure

Information flow in social groups

Wavelet correlations to reveal multiscale coupling in geophysical systems

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