6,169 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
Epidemics of Liquidity Shortages in Interbank Markets
Financial contagion from liquidity shocks has being recently ascribed as a
prominent driver of systemic risk in interbank lending markets. Building on
standard compartment models used in epidemics, in this work we develop an EDB
(Exposed-Distressed-Bankrupted) model for the dynamics of liquidity shocks
reverberation between banks, and validate it on electronic market for interbank
deposits data. We show that the interbank network was highly susceptible to
liquidity contagion at the beginning of the 2007/2008 global financial crisis,
and that the subsequent micro-prudential and liquidity hoarding policies
adopted by banks increased the network resilience to systemic risk---yet with
the undesired side effect of drying out liquidity from the market. We finally
show that the individual riskiness of a bank is better captured by its network
centrality than by its participation to the market, along with the currently
debated concept of "too interconnected to fail"
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
Phase transitions in contagion processes mediated by recurrent mobility patterns
Human mobility and activity patterns mediate contagion on many levels,
including the spatial spread of infectious diseases, diffusion of rumors, and
emergence of consensus. These patterns however are often dominated by specific
locations and recurrent flows and poorly modeled by the random diffusive
dynamics generally used to study them. Here we develop a theoretical framework
to analyze contagion within a network of locations where individuals recall
their geographic origins. We find a phase transition between a regime in which
the contagion affects a large fraction of the system and one in which only a
small fraction is affected. This transition cannot be uncovered by continuous
deterministic models due to the stochastic features of the contagion process
and defines an invasion threshold that depends on mobility parameters,
providing guidance for controlling contagion spread by constraining mobility
processes. We recover the threshold behavior by analyzing diffusion processes
mediated by real human commuting data.Comment: 20 pages of Main Text including 4 figures, 7 pages of Supplementary
Information; Nature Physics (2011
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
Dynamical Systems on Networks: A Tutorial
We give a tutorial for the study of dynamical systems on networks. We focus
especially on "simple" situations that are tractable analytically, because they
can be very insightful and provide useful springboards for the study of more
complicated scenarios. We briefly motivate why examining dynamical systems on
networks is interesting and important, and we then give several fascinating
examples and discuss some theoretical results. We also briefly discuss
dynamical systems on dynamical (i.e., time-dependent) networks, overview
software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than
original version, some reorganization and also more pointers to interesting
direction
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