4,914 research outputs found
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
A framework for epidemic spreading in multiplex networks of metapopulations
We propose a theoretical framework for the study of epidemics in structured
metapopulations, with heterogeneous agents, subjected to recurrent mobility
patterns. We propose to represent the heterogeneity in the composition of the
metapopulations as layers in a multiplex network, where nodes would correspond
to geographical areas and layers account for the mobility patterns of agents of
the same class. We analyze both the classical Susceptible-Infected-Susceptible
and the Susceptible-Infected-Removed epidemic models within this framework, and
compare macroscopic and microscopic indicators of the spreading process with
extensive Monte Carlo simulations. Our results are in excellent agreement with
the simulations. We also derive an exact expression of the epidemic threshold
on this general framework revealing a non-trivial dependence on the mobility
parameter. Finally, we use this new formalism to address the spread of diseases
in real cities, specifically in the city of Medellin, Colombia, whose
population is divided into six socio-economic classes, each one identified with
a layer in this multiplex formalism.Comment: 13 pages, 11 figure
Analytical computation of the epidemic threshold on temporal networks
The time variation of contacts in a networked system may fundamentally alter
the properties of spreading processes and affect the condition for large-scale
propagation, as encoded in the epidemic threshold. Despite the great interest
in the problem for the physics, applied mathematics, computer science and
epidemiology communities, a full theoretical understanding is still missing and
currently limited to the cases where the time-scale separation holds between
spreading and network dynamics or to specific temporal network models. We
consider a Markov chain description of the Susceptible-Infectious-Susceptible
process on an arbitrary temporal network. By adopting a multilayer perspective,
we develop a general analytical derivation of the epidemic threshold in terms
of the spectral radius of a matrix that encodes both network structure and
disease dynamics. The accuracy of the approach is confirmed on a set of
temporal models and empirical networks and against numerical results. In
addition, we explore how the threshold changes when varying the overall time of
observation of the temporal network, so as to provide insights on the optimal
time window for data collection of empirical temporal networked systems. Our
framework is both of fundamental and practical interest, as it offers novel
understanding of the interplay between temporal networks and spreading
dynamics.Comment: 22 pages, 6 figure
The physics of spreading processes in multilayer networks
The study of networks plays a crucial role in investigating the structure,
dynamics, and function of a wide variety of complex systems in myriad
disciplines. Despite the success of traditional network analysis, standard
networks provide a limited representation of complex systems, which often
include different types of relationships (i.e., "multiplexity") among their
constituent components and/or multiple interacting subsystems. Such structural
complexity has a significant effect on both dynamics and function. Throwing
away or aggregating available structural information can generate misleading
results and be a major obstacle towards attempts to understand complex systems.
The recent "multilayer" approach for modeling networked systems explicitly
allows the incorporation of multiplexity and other features of realistic
systems. On one hand, it allows one to couple different structural
relationships by encoding them in a convenient mathematical object. On the
other hand, it also allows one to couple different dynamical processes on top
of such interconnected structures. The resulting framework plays a crucial role
in helping achieve a thorough, accurate understanding of complex systems. The
study of multilayer networks has also revealed new physical phenomena that
remain hidden when using ordinary graphs, the traditional network
representation. Here we survey progress towards attaining a deeper
understanding of spreading processes on multilayer networks, and we highlight
some of the physical phenomena related to spreading processes that emerge from
multilayer structure.Comment: 25 pages, 4 figure
Epidemic model with isolation in multilayer networks
The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all the research the isolation of infected individuals is disregarded. Hence we focus our study in an epidemic model in a two-layer network and we use an isolation parameter w to measure the effect of quarantining infected individuals from both layers during an isolation period tw. We call this process the Susceptible-Infected-Isolated-Recovered (SIIR) model. Using the framework of link percolation we find that isolation increases the critical epidemic threshold of the disease because the time in which infection can spread is reduced. In this scenario we find that this threshold increases with w and tw. When the isolation period is maximum there is a critical threshold for w above which the disease never becomes an epidemic. We simulate the process and find an excellent agreement with the theoretical results.We thank the NSF (grants CMMI 1125290 and CHE-1213217) and the Keck Foundation for financial support. LGAZ and LAB wish to thank to UNMdP and FONCyT (Pict 0429/2013) for financial support. (CMMI 1125290 - NSF; CHE-1213217 - NSF; Keck Foundation; UNMdP; Pict 0429/2013 - FONCyT)Published versio
Epidemic Model with Isolation in Multilayer Networks
The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the
propagation of such airborne diseases as influenza A (H1N1). Although the SIR
model has recently been studied in a multilayer networks configuration, in
almost all the research the isolation of infected individuals is disregarded.
Hence we focus our study in an epidemic model in a two-layer network, and we
use an isolation parameter to measure the effect of isolating infected
individuals from both layers during an isolation period. We call this process
the Susceptible-Infected-Isolated-Recovered () model. The isolation
reduces the transmission of the disease because the time in which infection can
spread is reduced. In this scenario we find that the epidemic threshold
increases with the isolation period and the isolation parameter. When the
isolation period is maximum there is a threshold for the isolation parameter
above which the disease never becomes an epidemic. We also find that epidemic
models, like overestimate the theoretical risk of infection. Finally, our
model may provide a foundation for future research to study the temporal
evolution of the disease calibrating our model with real data.Comment: 18 pages, 5 figures.Accepted in Scientific Report
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