75,337 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
Network centrality: an introduction
Centrality is a key property of complex networks that influences the behavior
of dynamical processes, like synchronization and epidemic spreading, and can
bring important information about the organization of complex systems, like our
brain and society. There are many metrics to quantify the node centrality in
networks. Here, we review the main centrality measures and discuss their main
features and limitations. The influence of network centrality on epidemic
spreading and synchronization is also pointed out in this chapter. Moreover, we
present the application of centrality measures to understand the function of
complex systems, including biological and cortical networks. Finally, we
discuss some perspectives and challenges to generalize centrality measures for
multilayer and temporal networks.Comment: Book Chapter in "From nonlinear dynamics to complex systems: A
Mathematical modeling approach" by Springe
Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks
We present a quenched mean-field (QMF) theory for the dynamics of the
susceptible-infected-susceptible (SIS) epidemic model on complex networks where
dynamical correlations between connected vertices are taken into account by
means of a pair approximation. We present analytical expressions of the
epidemic thresholds in the star and wheel graphs and in random regular
networks. For random networks with a power law degree distribution, the
thresholds are numerically determined via an eigenvalue problem. The pair and
one-vertex QMF theories yield the same scaling for the thresholds as functions
of the network size. However, comparisons with quasi-stationary simulations of
the SIS dynamics on large networks show that the former is quantitatively much
more accurate than the latter. Our results demonstrate the central role played
by dynamical correlations on the epidemic spreading and introduce an efficient
way to theoretically access the thresholds of very large networks that can be
extended to dynamical processes in general.Comment: 6 pages, 6 figure
Dynamic Behavior of Interacting between Epidemics and Cascades on Heterogeneous Networks
Epidemic spreading and cascading failure are two important dynamical
processes over complex networks. They have been investigated separately for a
long history. But in the real world, these two dynamics sometimes may interact
with each other. In this paper, we explore a model combined with SIR epidemic
spreading model and local loads sharing cascading failure model. There exists a
critical value of tolerance parameter that whether the epidemic with high
infection probability can spread out and infect a fraction of the network in
this model. When the tolerance parameter is smaller than the critical value,
cascading failure cuts off abundant of paths and blocks the spreading of
epidemic locally. While the tolerance parameter is larger than the critical
value, epidemic spreads out and infects a fraction of the network. A method for
estimating the critical value is proposed. In simulation, we verify the
effectiveness of this method in Barab\'asi-Albert (BA) networks
Optimized Gillespie algorithms for the simulation of Markovian epidemic processes on large and heterogeneous networks
Numerical simulation of continuous-time Markovian processes is an essential
and widely applied tool in the investigation of epidemic spreading on complex
networks. Due to the high heterogeneity of the connectivity structure through
which epidemics is transmitted, efficient and accurate implementations of
generic epidemic processes are not trivial and deviations from statistically
exact prescriptions can lead to uncontrolled biases. Based on the Gillespie
algorithm (GA), in which only steps that change the state are considered, we
develop numerical recipes and describe their computer implementations for
statistically exact and computationally efficient simulations of generic
Markovian epidemic processes aiming at highly heterogeneous and large networks.
The central point of the recipes investigated here is to include phantom
processes, that do not change the states but do count for time increments. We
compare the efficiencies for the susceptible-infected-susceptible, contact
process and susceptible-infected-recovered models, that are particular cases of
a generic model considered here. We numerically confirm that the simulation
outcomes of the optimized algorithms are statistically indistinguishable from
the original GA and can be several orders of magnitude more efficient.Comment: 12 pages, 9 figure
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