1,576 research outputs found
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
Epidemic Thresholds with External Agents
We study the effect of external infection sources on phase transitions in
epidemic processes. In particular, we consider an epidemic spreading on a
network via the SIS/SIR dynamics, which in addition is aided by external agents
- sources unconstrained by the graph, but possessing a limited infection rate
or virulence. Such a model captures many existing models of externally aided
epidemics, and finds use in many settings - epidemiology, marketing and
advertising, network robustness, etc. We provide a detailed characterization of
the impact of external agents on epidemic thresholds. In particular, for the
SIS model, we show that any external infection strategy with constant virulence
either fails to significantly affect the lifetime of an epidemic, or at best,
sustains the epidemic for a lifetime which is polynomial in the number of
nodes. On the other hand, a random external-infection strategy, with rate
increasing linearly in the number of infected nodes, succeeds under some
conditions to sustain an exponential epidemic lifetime. We obtain similar sharp
thresholds for the SIR model, and discuss the relevance of our results in a
variety of settings.Comment: 12 pages, 2 figures (to appear in INFOCOM 2014
Relating Topological Determinants of Complex Networks to Their Spectral Properties: Structural and Dynamical Effects
The largest eigenvalue of a network's adjacency matrix and its associated
principal eigenvector are key elements for determining the topological
structure and the properties of dynamical processes mediated by it. We present
a physically grounded expression relating the value of the largest eigenvalue
of a given network to the largest eigenvalue of two network subgraphs,
considered as isolated: The hub with its immediate neighbors and the densely
connected set of nodes with maximum -core index. We validate this formula
showing that it predicts with good accuracy the largest eigenvalue of a large
set of synthetic and real-world topologies. We also present evidence of the
consequences of these findings for broad classes of dynamics taking place on
the networks. As a byproduct, we reveal that the spectral properties of
heterogeneous networks built according to the linear preferential attachment
model are qualitatively different from those of their static counterparts.Comment: 18 pages, 13 figure
Griffiths phases in infinite-dimensional, non-hierarchical modular networks
Griffiths phases (GPs), generated by the heterogeneities on modular networks,
have recently been suggested to provide a mechanism, rid of fine parameter
tuning, to explain the critical behavior of complex systems. One conjectured
requirement for systems with modular structures was that the network of modules
must be hierarchically organized and possess finite dimension. We investigate
the dynamical behavior of an activity spreading model, evolving on
heterogeneous random networks with highly modular structure and organized
non-hierarchically. We observe that loosely coupled modules act as effective
rare-regions, slowing down the extinction of activation. As a consequence, we
find extended control parameter regions with continuously changing dynamical
exponents for single network realizations, preserved after finite size
analyses, as in a real GP. The avalanche size distributions of spreading events
exhibit robust power-law tails. Our findings relax the requirement of
hierarchical organization of the modular structure, which can help to
rationalize the criticality of modular systems in the framework of GPs.Comment: 14 pages, 8 figure
Sufficient conditions of endemic threshold on metapopulation networks
In this paper, we focus on susceptible-infected-susceptible dynamics on
metapopulation networks, where nodes represent subpopulations, and where agents
diffuse and interact. Recent studies suggest that heterogeneous network
structure between elements plays an important role in determining the threshold
of infection rate at the onset of epidemics, a fundamental quantity governing
the epidemic dynamics. We consider the general case in which the infection rate
at each node depends on its population size, as shown in recent empirical
observations. We first prove that a sufficient condition for the endemic
threshold (i.e., its upper bound), previously derived based on a mean-field
approximation of network structure, also holds true for arbitrary networks. We
also derive an improved condition showing that networks with the rich-club
property (i.e., high connectivity between nodes with a large number of links)
are more prone to disease spreading. The dependency of infection rate on
population size introduces a considerable difference between this upper bound
and estimates based on mean-field approximations, even when degree-degree
correlations are considered. We verify the theoretical results with numerical
simulations.Comment: 32 pages, 5 figure
Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks
We provide numerical evidence for slow dynamics of the
susceptible-infected-susceptible model evolving on finite-size random networks
with power-law degree distributions. Extensive simulations were done by
averaging the activity density over many realizations of networks. We
investigated the effects of outliers in both highly fluctuating (natural
cutoff) and non-fluctuating (hard cutoff) most connected vertices. Logarithmic
and power-law decays in time were found for natural and hard cutoffs,
respectively. This happens in extended regions of the control parameter space
, suggesting Griffiths effects, induced by the
topological inhomogeneities. Optimal fluctuation theory considering
sample-to-sample fluctuations of the pseudo thresholds is presented to explain
the observed slow dynamics. A quasistationary analysis shows that response
functions remain bounded at . We argue these to be signals of a
smeared transition. However, in the thermodynamic limit the Griffiths effects
loose their relevancy and have a conventional critical point at .
Since many real networks are composed by heterogeneous and weakly connected
modules, the slow dynamics found in our analysis of independent and finite
networks can play an important role for the deeper understanding of such
systems.Comment: 10 pages, 8 figure
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