887 research outputs found
Optimal Vaccine Allocation to Control Epidemic Outbreaks in Arbitrary Networks
We consider the problem of controlling the propagation of an epidemic
outbreak in an arbitrary contact network by distributing vaccination resources
throughout the network. We analyze a networked version of the
Susceptible-Infected-Susceptible (SIS) epidemic model when individuals in the
network present different levels of susceptibility to the epidemic. In this
context, controlling the spread of an epidemic outbreak can be written as a
spectral condition involving the eigenvalues of a matrix that depends on the
network structure and the parameters of the model. We study the problem of
finding the optimal distribution of vaccines throughout the network to control
the spread of an epidemic outbreak. We propose a convex framework to find
cost-optimal distribution of vaccination resources when different levels of
vaccination are allowed. We also propose a greedy approach with quality
guarantees for the case of all-or-nothing vaccination. We illustrate our
approaches with numerical simulations in a real social network
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
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 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
Worst-Case Scenarios for Greedy, Centrality-Based Network Protection Strategies
The task of allocating preventative resources to a computer network in order
to protect against the spread of viruses is addressed. Virus spreading dynamics
are described by a linearized SIS model and protection is framed by an
optimization problem which maximizes the rate at which a virus in the network
is contained given finite resources. One approach to problems of this type
involve greedy heuristics which allocate all resources to the nodes with large
centrality measures. We address the worst case performance of such greedy
algorithms be constructing networks for which these greedy allocations are
arbitrarily inefficient. An example application is presented in which such a
worst case network might arise naturally and our results are verified
numerically by leveraging recent results which allow the exact optimal solution
to be computed via geometric programming
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