20 research outputs found
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
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
Network analysis of pig movements: Loyalty patterns and contact chains of different holding types in Denmark
Understanding animal movements is an important factor for the development of meaningful surveillance and control programs, but also for the development of disease spread models. We analysed the Danish pig movement network using static and temporal network analysis tools to provide deeper insight in the connection between holdings dealing with pigs, such as breeding and multiplier herds, production herds, slaughterhouses or traders. Pig movements, which occurred between 1st January 2006 and 31st December 2015 in Denmark, were summarized to investigate temporal trends such as the number of active holdings, the number of registered movements and the number of pigs moved. To identify holdings and holding types with potentially higher risk for introduction or spread of diseases via pig movements, we determined loyalty patterns, annual network components and contact chains for the 24 registered holding types. The total number of active holdings as well as the number of pig movements decreased during the study period while the holding sizes increased. Around 60-90% of connections between two pig holdings were present in two consecutive years and around one third of the connections persisted within the considered time period. Weaner herds showed the highest level of in-loyalty, whereas we observed an intermediate level of in-loyalty for all breeding sites and for production herds. Boar stations, production herds and trade herds showed a high level of out-loyalty. Production herds constituted the highest proportion of holdings in the largest strongly connected component. All production sites showed low levels of in-going contact chains and we observed a high level of out-going contact chain for breeding and multiplier herds. Except for livestock auctions, all transit sites also showed low levels of out-going contact chains. Our results reflect the pyramidal structure of the underlying network. Based on the considered disease, the time frame for the calculation of network measurements needs to be adapted. Using these adapted values for loyalty and contact chains might help to identify holdings with high potential of spreading diseases and thus limit the outbreak size or support control or eradication of the considered pathogen