2,635 research outputs found
Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic model
Data of physical contacts and face-to-face communications suggest temporally
varying networks as the media on which infections take place among humans and
animals. Epidemic processes on temporal networks are complicated by complexity
of both network structure and temporal dimensions. Theoretical approaches are
much needed for identifying key factors that affect dynamics of epidemics. In
particular, what factors make some temporal networks stronger media of
infection than other temporal networks is under debate. We develop a theory to
understand the susceptible-infected-susceptible epidemic model on arbitrary
temporal networks, where each contact is used for a finite duration. We show
that temporality of networks lessens the epidemic threshold such that
infections persist more easily in temporal networks than in their static
counterparts. We further show that the Lie commutator bracket of the adjacency
matrices at different times is a key determinant of the epidemic threshold in
temporal networks. The effect of temporality on the epidemic threshold, which
depends on a data set, is approximately predicted by the magnitude of a
commutator norm.Comment: 8 figures, 1 tabl
Spreading processes in Multilayer Networks
Several systems can be modeled as sets of interconnected networks or networks
with multiple types of connections, here generally called multilayer networks.
Spreading processes such as information propagation among users of an online
social networks, or the diffusion of pathogens among individuals through their
contact network, are fundamental phenomena occurring in these networks.
However, while information diffusion in single networks has received
considerable attention from various disciplines for over a decade, spreading
processes in multilayer networks is still a young research area presenting many
challenging research issues. In this paper we review the main models, results
and applications of multilayer spreading processes and discuss some promising
research directions.Comment: 21 pages, 3 figures, 4 table
Invited review: Epidemics on social networks
Since its first formulations almost a century ago, mathematical models for
disease spreading contributed to understand, evaluate and control the epidemic
processes.They promoted a dramatic change in how epidemiologists thought of the
propagation of infectious diseases.In the last decade, when the traditional
epidemiological models seemed to be exhausted, new types of models were
developed.These new models incorporated concepts from graph theory to describe
and model the underlying social structure.Many of these works merely produced a
more detailed extension of the previous results, but some others triggered a
completely new paradigm in the mathematical study of epidemic processes. In
this review, we will introduce the basic concepts of epidemiology, epidemic
modeling and networks, to finally provide a brief description of the most
relevant results in the field.Comment: 17 pages, 13 figure
Layer-switching cost and optimality in information spreading on multiplex networks
We study a model of information spreading on multiplex networks, in which
agents interact through multiple interaction channels (layers), say online vs.\
offline communication layers, subject to layer-switching cost for transmissions
across different interaction layers. The model is characterized by the
layer-wise path-dependent transmissibility over a contact, that is dynamically
determined dependently on both incoming and outgoing transmission layers. We
formulate an analytical framework to deal with such path-dependent
transmissibility and demonstrate the nontrivial interplay between the
multiplexity and spreading dynamics, including optimality. It is shown that the
epidemic threshold and prevalence respond to the layer-switching cost
non-monotonically and that the optimal conditions can change in abrupt
non-analytic ways, depending also on the densities of network layers and the
type of seed infections. Our results elucidate the essential role of
multiplexity that its explicit consideration should be crucial for realistic
modeling and prediction of spreading phenomena on multiplex social networks in
an era of ever-diversifying social interaction layers.Comment: 15 pages, 7 figure
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