23 research outputs found
Bursts of vertex activation and epidemics in evolving networks
The dynamic nature of contact patterns creates diverse temporal structures. In particular, empirical studies have shown that contact patterns follow heterogeneous inter-event time intervals, meaning that periods of high activity are followed by long periods of inactivity. To investigate the impact of these heterogeneities in the spread of infection from a theoretical perspective, we propose a stochastic model to generate temporal networks where vertices make instantaneous contacts following heterogeneous inter-event intervals, and may leave and enter the system. We study how these properties affect the prevalence of an infection and estimate , the number of secondary infections of an infectious individual in a completely susceptible population, by modeling simulated infections (SI and SIR) that co-evolve with the network structure. We find that heterogeneous contact patterns cause earlier and larger epidemics in the SIR model in comparison to homogeneous scenarios for a vast range of parameter values, while smaller epidemics may happen in some combinations of parameters. In the case of SI and heterogeneous patterns, the epidemics develop faster in the earlier stages followed by a slowdown in the asymptotic limit. For increasing vertex turnover rates, heterogeneous patterns generally cause higher prevalence in comparison to homogeneous scenarios with the same average inter-event interval. We find that is generally higher for heterogeneous patterns, except for sufficiently large infection duration and transmission probability
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
Bursting activity spreading through asymmetric interactions
People communicate with those who have the same background or share a common
interest by using a social networking service (SNS). News or messages propagate
through inhomogeneous connections in an SNS by sharing or facilitating
additional comments. Such human activity is known to lead to endogenous
bursting in the rate of message occurrences. We analyze a multi-dimensional
self-exciting process to reveal dependence of the bursting activity on the
topology of connections and the distribution of interaction strength on the
connections. We determine the critical conditions for the cases where
interaction strength is regulated at either the point of input or output for
each person. In the input regulation condition, the network may exhibit
bursting with infinitesimal interaction strength, if the dispersion of the
degrees diverges as in the scale-free networks. In contrast, in the output
regulation condition, the critical value of interaction strength, represented
by the average number of events added by a single event, is a constant
, independent of the degree dispersion. Thus, the
stability in human activity crucially depends on not only the topology of
connections but also the manner in which interactions are distributed among the
connections.Comment: 8 pages, 8 figure
Non-systemic transmission of tick-borne diseases: a network approach
Tick-Borne diseases can be transmitted via non-systemic (NS) transmission.
This occurs when tick gets the infection by co-feeding with infected ticks on
the same host resulting in a direct pathogen transmission between the vectors,
without infecting the host. This transmission is peculiar, as it does not
require any systemic infection of the host. The NS transmission is the main
efficient transmission for the persistence of the Tick-Borne Encephalitis virus
in nature. By describing the heterogeneous ticks aggregation on hosts through a
\hyphenation{dynamical} bipartite graphs representation, we are able to
mathematically define the NS transmission and to depict the epidemiological
conditions for the pathogen persistence. Despite the fact that the underlying
network is largely fragmented, analytical and computational results show that
the larger is the variability of the aggregation, and the easier is for the
pathogen to persist in the population.Comment: 15 pages, 4 figures, to be published in Communications in Nonlinear
Science and Numerical Simulatio
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
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
Burstiness and tie activation strategies in time-varying social networks
The recent developments in the field of social networks shifted the focus from static to dynamical representations, calling for new methods for their analysis and modelling. Observations in real social systems identified two main mechanisms that play a primary role in networks' evolution and influence ongoing spreading processes: the strategies individuals adopt when selecting between new or old social ties, and the bursty nature of the social activity setting the pace of these choices. We introduce a time-varying network model accounting both for ties selection and burstiness and we analytically study its phase diagram. The interplay of the two effects is non trivial and, interestingly, the effects of burstiness might be suppressed in regimes where individuals exhibit a strong preference towards previously activated ties. The results are tested against numerical simulations and compared with two empirical datasets with very good agreement. Consequently, the framework provides a principled method to classify the temporal features of real networks, and thus yields new insights to elucidate the effects of social dynamics on spreading processes