2,037 research outputs found
Traffic Control for Network Protection Against Spreading Processes
Epidemic outbreaks in human populations are facilitated by the underlying
transportation network. We consider strategies for containing a viral spreading
process by optimally allocating a limited budget to three types of protection
resources: (i) Traffic control resources, (ii), preventative resources and
(iii) corrective resources. Traffic control resources are employed to impose
restrictions on the traffic flowing across directed edges in the transportation
network. Preventative resources are allocated to nodes to reduce the
probability of infection at that node (e.g. vaccines), and corrective resources
are allocated to nodes to increase the recovery rate at that node (e.g.
antidotes). We assume these resources have monetary costs associated with them,
from which we formalize an optimal budget allocation problem which maximizes
containment of the infection. We present a polynomial time solution to the
optimal budget allocation problem using Geometric Programming (GP) for an
arbitrary weighted and directed contact network and a large class of resource
cost functions. We illustrate our approach by designing optimal traffic control
strategies to contain an epidemic outbreak that propagates through a real-world
air transportation network.Comment: arXiv admin note: text overlap with arXiv:1309.627
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
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
Optimal Resource Allocation for Network Protection Against Spreading Processes
We study the problem of containing spreading processes in arbitrary directed
networks by distributing protection resources throughout the nodes of the
network. We consider two types of protection resources are available: (i)
Preventive resources able to defend nodes against the spreading (such as
vaccines in a viral infection process), and (ii) corrective resources able to
neutralize the spreading after it has reached a node (such as antidotes). We
assume that both preventive and corrective resources have an associated cost
and study the problem of finding the cost-optimal distribution of resources
throughout the nodes of the network. We analyze these questions in the context
of viral spreading processes in directed networks. We study the following two
problems: (i) Given a fixed budget, find the optimal allocation of preventive
and corrective resources in the network to achieve the highest level of
containment, and (ii) when a budget is not specified, find the minimum budget
required to control the spreading process. We show that both resource
allocation problems can be solved in polynomial time using Geometric
Programming (GP) for arbitrary directed graphs of nonidentical nodes and a wide
class of cost functions. Furthermore, our approach allows to optimize
simultaneously over both preventive and corrective resources, even in the case
of cost functions being node-dependent. We illustrate our approach by designing
optimal protection strategies to contain an epidemic outbreak that propagates
through an air transportation network
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