596 research outputs found
Disease spread over randomly switched large-scale networks
In this paper we study disease spread over a randomly switched network, which
is modeled by a stochastic switched differential equation based on the so
called -intertwined model for disease spread over static networks. Assuming
that all the edges of the network are independently switched, we present
sufficient conditions for the convergence of infection probability to zero.
Though the stability theory for switched linear systems can naively derive a
necessary and sufficient condition for the convergence, the condition cannot be
used for large-scale networks because, for a network with agents, it
requires computing the maximum real eigenvalue of a matrix of size exponential
in . On the other hand, our conditions that are based also on the spectral
theory of random matrices can be checked by computing the maximum real
eigenvalue of a matrix of size exactly
Epidemic Threshold in Continuous-Time Evolving Networks
Current understanding of the critical outbreak condition on temporal networks
relies on approximations (time scale separation, discretization) that may bias
the results. We propose a theoretical framework to compute the epidemic
threshold in continuous time through the infection propagator approach. We
introduce the {\em weak commutation} condition allowing the interpretation of
annealed networks, activity-driven networks, and time scale separation into one
formalism. Our work provides a coherent connection between discrete and
continuous time representations applicable to realistic scenarios.Comment: 13 pages, 2 figure
Immunization strategies for epidemic processes in time-varying contact networks
Spreading processes represent a very efficient tool to investigate the
structural properties of networks and the relative importance of their
constituents, and have been widely used to this aim in static networks. Here we
consider simple disease spreading processes on empirical time-varying networks
of contacts between individuals, and compare the effect of several immunization
strategies on these processes. An immunization strategy is defined as the
choice of a set of nodes (individuals) who cannot catch nor transmit the
disease. This choice is performed according to a certain ranking of the nodes
of the contact network. We consider various ranking strategies, focusing in
particular on the role of the training window during which the nodes'
properties are measured in the time-varying network: longer training windows
correspond to a larger amount of information collected and could be expected to
result in better performances of the immunization strategies. We find instead
an unexpected saturation in the efficiency of strategies based on nodes'
characteristics when the length of the training window is increased, showing
that a limited amount of information on the contact patterns is sufficient to
design efficient immunization strategies. This finding is balanced by the large
variations of the contact patterns, which strongly alter the importance of
nodes from one period to the next and therefore significantly limit the
efficiency of any strategy based on an importance ranking of nodes. We also
observe that the efficiency of strategies that include an element of randomness
and are based on temporally local information do not perform as well but are
largely independent on the amount of information available
Cost-efficient vaccination protocols for network epidemiology
We investigate methods to vaccinate contact networks -- i.e. removing nodes
in such a way that disease spreading is hindered as much as possible -- with
respect to their cost-efficiency. Any real implementation of such protocols
would come with costs related both to the vaccination itself, and gathering of
information about the network. Disregarding this, we argue, would lead to
erroneous evaluation of vaccination protocols. We use the
susceptible-infected-recovered model -- the generic model for diseases making
patients immune upon recovery -- as our disease-spreading scenario, and analyze
outbreaks on both empirical and model networks. For different relative costs,
different protocols dominate. For high vaccination costs and low costs of
gathering information, the so-called acquaintance vaccination is the most cost
efficient. For other parameter values, protocols designed for query-efficient
identification of the network's largest degrees are most efficient
From temporal network data to the dynamics of social relationships
Networks are well-established representations of social systems, and temporal
networks are widely used to study their dynamics. Temporal network data often
consist in a succession of static networks over consecutive time windows whose
length, however, is arbitrary, not necessarily corresponding to any intrinsic
timescale of the system. Moreover, the resulting view of social network
evolution is unsatisfactory: short time windows contain little information,
whereas aggregating over large time windows blurs the dynamics. Going from a
temporal network to a meaningful evolving representation of a social network
therefore remains a challenge. Here we introduce a framework to that purpose:
transforming temporal network data into an evolving weighted network where the
weights of the links between individuals are updated at every interaction. Most
importantly, this transformation takes into account the interdependence of
social relationships due to the finite attention capacities of individuals:
each interaction between two individuals not only reinforces their mutual
relationship but also weakens their relationships with others. We study a
concrete example of such a transformation and apply it to several data sets of
social interactions. Using temporal contact data collected in schools, we show
how our framework highlights specificities in their structure and temporal
organization. We then introduce a synthetic perturbation into a data set of
interactions in a group of baboons to show that it is possible to detect a
perturbation in a social group on a wide range of timescales and parameters.
Our framework brings new perspectives to the analysis of temporal social
networks
Networks and the epidemiology of infectious disease
The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues
Quantifying the effect of temporal resolution on time-varying networks
Time-varying networks describe a wide array of systems whose constituents and interactions evolve over time. They are defined by an ordered stream of interactions between nodes, yet they are often represented in terms of a sequence of static networks, each aggregating all edges and nodes present in a time interval of size Δt. In this work we quantify the impact of an arbitrary Δt on the description of a dynamical process taking place upon a time-varying network. We focus on the elementary random walk, and put forth a simple mathematical framework that well describes the behavior observed on real datasets. The analytical description of the bias introduced by time integrating techniques represents a step forward in the correct characterization of dynamical processes on time-varying graphs
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