176 research outputs found
A Convex Framework for Optimal Investment on Disease Awareness in Social Networks
We consider the problem of controlling the propagation of an epidemic
outbreak in an arbitrary network of contacts by investing on disease awareness
throughout the network. We model the effect of agent awareness on the dynamics
of an epidemic using the SAIS epidemic model, an extension of the SIS epidemic
model that includes a state of "awareness". This model allows to derive a
condition to control the spread of an epidemic outbreak in terms of the
eigenvalues of a matrix that depends on the network structure and the
parameters of the model. We study the problem of finding the cost-optimal
investment on disease awareness throughout the network when the cost function
presents some realistic properties. We propose a convex framework to find
cost-optimal allocation of resources. We validate our results with numerical
simulations in a real online social network.Comment: IEEE GlobalSIP Symposium on Network Theor
Effect of Coupling on the Epidemic Threshold in Interconnected Complex Networks: A Spectral Analysis
In epidemic modeling, the term infection strength indicates the ratio of
infection rate and cure rate. If the infection strength is higher than a
certain threshold -- which we define as the epidemic threshold - then the
epidemic spreads through the population and persists in the long run. For a
single generic graph representing the contact network of the population under
consideration, the epidemic threshold turns out to be equal to the inverse of
the spectral radius of the contact graph. However, in a real world scenario it
is not possible to isolate a population completely: there is always some
interconnection with another network, which partially overlaps with the contact
network. Results for epidemic threshold in interconnected networks are limited
to homogeneous mixing populations and degree distribution arguments. In this
paper, we adopt a spectral approach. We show how the epidemic threshold in a
given network changes as a result of being coupled with another network with
fixed infection strength. In our model, the contact network and the
interconnections are generic. Using bifurcation theory and algebraic graph
theory, we rigorously derive the epidemic threshold in interconnected networks.
These results have implications for the broad field of epidemic modeling and
control. Our analytical results are supported by numerical simulations.Comment: 7 page
Exact Coupling Threshold for Structural Transition in Interconnected Networks
Interconnected networks are mathematical representation of systems where two
or more simple networks are coupled to each other. Depending on the coupling
weight between the two components, the interconnected network can function in
two regimes: one where the two networks are structurally distinguishable, and
one where they are not. The coupling threshold--denoting this structural
transition--is one of the most crucial concepts in interconnected networks.
Yet, current information about the coupling threshold is limited. This letter
presents an analytical expression for the exact value of the coupling threshold
and outlines network interrelation implications
Robustness surfaces of complex networks
Despite the robustness of complex networks has been extensively studied in
the last decade, there still lacks a unifying framework able to embrace all the
proposed metrics. In the literature there are two open issues related to this
gap: (a) how to dimension several metrics to allow their summation and (b) how
to weight each of the metrics. In this work we propose a solution for the two
aforementioned problems by defining the -value and introducing the concept
of \emph{robustness surface} (). The rationale of our proposal is to
make use of Principal Component Analysis (PCA). We firstly adjust to 1 the
initial robustness of a network. Secondly, we find the most informative
robustness metric under a specific failure scenario. Then, we repeat the
process for several percentage of failures and different realizations of the
failure process. Lastly, we join these values to form the robustness surface,
which allows the visual assessment of network robustness variability. Results
show that a network presents different robustness surfaces (i.e., dissimilar
shapes) depending on the failure scenario and the set of metrics. In addition,
the robustness surface allows the robustness of different networks to be
compared.Comment: submitted to Scientific Report
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