61 research outputs found
Impact of Clustering on Diffusions and Contagions in Random Networks
International audienceMotivated by the analysis of social networks, we study a model of network that has both a tunable degree distribution and a tunable clustering coefficient. We compute the asymptotic (as the size of the population tends to infinity) for the number of acquaintances and the clustering for this model. We analyze a contagion model with threshold effects and obtain conditions for the existence of a large cascade. We also analyze a diffusion process with a given probability of contagion. In both cases, we characterize conditions under which a global cascade is possible
Contagions in Random Networks with Overlapping Communities
We consider a threshold epidemic model on a clustered random graph with
overlapping communities. In other words, our epidemic model is such that an
individual becomes infected as soon as the proportion of her infected neighbors
exceeds the threshold q of the epidemic. In our random graph model, each
individual can belong to several communities. The distributions for the
community sizes and the number of communities an individual belongs to are
arbitrary.
We consider the case where the epidemic starts from a single individual, and
we prove a phase transition (when the parameter q of the model varies) for the
appearance of a cascade, i.e. when the epidemic can be propagated to an
infinite part of the population. More precisely, we show that our epidemic is
entirely described by a multi-type (and alternating) branching process, and
then we apply Sevastyanov's theorem about the phase transition of multi-type
Galton-Watson branching processes. In addition, we compute the entries of the
matrix whose largest eigenvalue gives the phase transition.Comment: Minor modifications for the second version: added comments (end of
Section 3.2, beginning of Section 5.3); moved remark (end of Section 3.1,
beginning of Section 4.1); corrected typos; changed titl
Overcoming vaccine hesitancy by multiplex social network targeting: An analysis of targeting algorithms and implications
Incorporating social factors into disease prevention and control efforts is
an important undertaking of behavioral epidemiology. The interplay between
disease transmission and human health behaviors, such as vaccine uptake,
results in complex dynamics of biological and social contagions. Maximizing
intervention adoptions via network-based targeting algorithms by harnessing the
power of social contagion for behavior and attitude changes largely remains a
challenge. Here we address this issue by considering a multiplex network
setting. Individuals are situated on two layers of networks: the disease
transmission network layer and the peer influence network layer. The disease
spreads through direct close contacts while vaccine views and uptake behaviors
spread interpersonally within a potentially virtual network. The results of our
comprehensive simulations show that network-based targeting with pro-vaccine
supporters as initial seeds significantly influences vaccine adoption rates and
reduces the extent of an epidemic outbreak. Network targeting interventions are
much more effective by selecting individuals with a central position in the
opinion network as compared to those grouped in a community or connected
professionally. Our findings provide insight into network-based interventions
to increase vaccine confidence and demand during an ongoing epidemic.Comment: 16 pages, 8 figures. Comments are welcom
Topological data analysis of contagion maps for examining spreading processes on networks
Social and biological contagions are influenced by the spatial embeddedness
of networks. Historically, many epidemics spread as a wave across part of the
Earth's surface; however, in modern contagions long-range edges -- for example,
due to airline transportation or communication media -- allow clusters of a
contagion to appear in distant locations. Here we study the spread of
contagions on networks through a methodology grounded in topological data
analysis and nonlinear dimension reduction. We construct "contagion maps" that
use multiple contagions on a network to map the nodes as a point cloud. By
analyzing the topology, geometry, and dimensionality of manifold structure in
such point clouds, we reveal insights to aid in the modeling, forecast, and
control of spreading processes. Our approach highlights contagion maps also as
a viable tool for inferring low-dimensional structure in networks.Comment: Main Text and Supplementary Informatio
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