1,423 research outputs found
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
Griffiths phases in infinite-dimensional, non-hierarchical modular networks
Griffiths phases (GPs), generated by the heterogeneities on modular networks,
have recently been suggested to provide a mechanism, rid of fine parameter
tuning, to explain the critical behavior of complex systems. One conjectured
requirement for systems with modular structures was that the network of modules
must be hierarchically organized and possess finite dimension. We investigate
the dynamical behavior of an activity spreading model, evolving on
heterogeneous random networks with highly modular structure and organized
non-hierarchically. We observe that loosely coupled modules act as effective
rare-regions, slowing down the extinction of activation. As a consequence, we
find extended control parameter regions with continuously changing dynamical
exponents for single network realizations, preserved after finite size
analyses, as in a real GP. The avalanche size distributions of spreading events
exhibit robust power-law tails. Our findings relax the requirement of
hierarchical organization of the modular structure, which can help to
rationalize the criticality of modular systems in the framework of GPs.Comment: 14 pages, 8 figure
Variability of Contact Process in Complex Networks
We study numerically how the structures of distinct networks influence the
epidemic dynamics in contact process. We first find that the variability
difference between homogeneous and heterogeneous networks is very narrow,
although the heterogeneous structures can induce the lighter prevalence.
Contrary to non-community networks, strong community structures can cause the
secondary outbreak of prevalence and two peaks of variability appeared.
Especially in the local community, the extraordinarily large variability in
early stage of the outbreak makes the prediction of epidemic spreading hard.
Importantly, the bridgeness plays a significant role in the predictability,
meaning the further distance of the initial seed to the bridgeness, the less
accurate the predictability is. Also, we investigate the effect of different
disease reaction mechanisms on variability, and find that the different
reaction mechanisms will result in the distinct variabilities at the end of
epidemic spreading.Comment: 6 pages, 4 figure
Spectral properties of the hierarchical product of graphs
The hierarchical product of two graphs represents a natural way to build a
larger graph out of two smaller graphs with less regular and therefore more
heterogeneous structure than the Cartesian product. Here we study the
eigenvalue spectrum of the adjacency matrix of the hierarchical product of two
graphs. Introducing a coupling parameter describing the relative contribution
of each of the two smaller graphs, we perform an asymptotic analysis for the
full spectrum of eigenvalues of the adjacency matrix of the hierarchical
product. Specifically, we derive the exact limit points for each eigenvalue in
the limits of small and large coupling, as well as the leading-order relaxation
to these values in terms of the eigenvalues and eigenvectors of the two smaller
graphs. Given its central roll in the structural and dynamical properties of
networks, we study in detail the Perron-Frobenius, or largest, eigenvalue.
Finally, as an example application we use our theory to predict the epidemic
threshold of the Susceptible-Infected-Susceptible model on a hierarchical
product of two graphs
Optimal curing policy for epidemic spreading over a community network with heterogeneous population
The design of an efficient curing policy, able to stem an epidemic process at
an affordable cost, has to account for the structure of the population contact
network supporting the contagious process. Thus, we tackle the problem of
allocating recovery resources among the population, at the lowest cost possible
to prevent the epidemic from persisting indefinitely in the network.
Specifically, we analyze a susceptible-infected-susceptible epidemic process
spreading over a weighted graph, by means of a first-order mean-field
approximation. First, we describe the influence of the contact network on the
dynamics of the epidemics among a heterogeneous population, that is possibly
divided into communities. For the case of a community network, our
investigation relies on the graph-theoretical notion of equitable partition; we
show that the epidemic threshold, a key measure of the network robustness
against epidemic spreading, can be determined using a lower-dimensional
dynamical system. Exploiting the computation of the epidemic threshold, we
determine a cost-optimal curing policy by solving a convex minimization
problem, which possesses a reduced dimension in the case of a community
network. Lastly, we consider a two-level optimal curing problem, for which an
algorithm is designed with a polynomial time complexity in the network size.Comment: to be published on Journal of Complex Network
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
Pair quenched mean-field theory for the susceptible-infected-susceptible model on complex networks
We present a quenched mean-field (QMF) theory for the dynamics of the
susceptible-infected-susceptible (SIS) epidemic model on complex networks where
dynamical correlations between connected vertices are taken into account by
means of a pair approximation. We present analytical expressions of the
epidemic thresholds in the star and wheel graphs and in random regular
networks. For random networks with a power law degree distribution, the
thresholds are numerically determined via an eigenvalue problem. The pair and
one-vertex QMF theories yield the same scaling for the thresholds as functions
of the network size. However, comparisons with quasi-stationary simulations of
the SIS dynamics on large networks show that the former is quantitatively much
more accurate than the latter. Our results demonstrate the central role played
by dynamical correlations on the epidemic spreading and introduce an efficient
way to theoretically access the thresholds of very large networks that can be
extended to dynamical processes in general.Comment: 6 pages, 6 figure
Coupled effects of local movement and global interaction on contagion
By incorporating segregated spatial domain and individual-based linkage into
the SIS (susceptible-infected-susceptible) model, we investigate the coupled
effects of random walk and intragroup interaction on contagion. Compared with
the situation where only local movement or individual-based linkage exists, the
coexistence of them leads to a wider spread of infectious disease. The roles of
narrowing segregated spatial domain and reducing mobility in epidemic control
are checked, these two measures are found to be conducive to curbing the spread
of infectious disease. Considering heterogeneous time scales between local
movement and global interaction, a log-log relation between the change in the
number of infected individuals and the timescale is found. A theoretical
analysis indicates that the evolutionary dynamics in the present model is
related to the encounter probability and the encounter time. A functional
relation between the epidemic threshold and the ratio of shortcuts, and a
functional relation between the encounter time and the timescale are
found
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