1,878 research outputs found
A Convex Framework for Epidemic Control in Networks
With networks becoming pervasive, research attention on dynamics of epidemic models in networked populations has increased. While a number of well understood epidemic spreading models have been developed, little to no attention has been paid to epidemic control strategies; beyond heuristics usually based on network centrality measures. Since epidemic control resources are typically limited, the problem of optimally allocating resources to control an outbreak becomes of interest.
Existing literature considered homogeneous networks, limited the discussion to undirected networks, and largely proposed network centrality-based resource allocation strategies.
In this thesis, we consider the well-known Susceptible-Infected-Susceptible spreading model and study the problem of minimum cost resource allocation to control an epidemic outbreak in a networked population. First, we briefly present a heuristic that outperforms network centrality-based algorithms on a stylized version of the problem previously studied in the literature. We then solve the epidemic control problem via a convex optimization framework on weighted, directed networks comprising heterogeneous nodes. Based on our spreading model, we express the problem of controlling an epidemic outbreak in terms of spectral conditions involving the Perron-Frobenius eigenvalue. This enables formulation of the epidemic control problem as a Geometric Program (GP), for which we derive a convex characterization guaranteeing existence of an optimal solution. We consider two formulations of the epidemic control problem -- the first seeks an optimal vaccine and antidote allocation strategy given a constraint on the rate at which the epidemic comes under control. The second formulation seeks to find an optimal allocation strategy given a budget on the resources. The solution framework for both formulations also allows for control of an epidemic outbreak on networks that are not necessarily strongly connected. The thesis further proposes a fully distributed solution to the epidemic control problem via a Distributed Alternating Direction Method of Multipliers (ADMM) algorithm. Our distributed solution enables each node to locally compute its optimum allocation of vaccines and antidotes needed to collectively globally contain the spread of an outbreak, via local exchange of information with its neighbors. Contrasting previous literature, our problem is a constrained optimization problem associated with a directed network comprising non-identical agents. For the different problem formulations considered, illustrations that validate our solutions are presented. This thesis, in sum, proposes a paradigm shift from heuristics towards a convex framework for contagion control in networked populations
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 Resource Allocation Over Time and Degree Classes for Maximizing Information Dissemination in Social Networks
We study the optimal control problem of allocating campaigning resources over
the campaign duration and degree classes in a social network. Information
diffusion is modeled as a Susceptible-Infected epidemic and direct recruitment
of susceptible nodes to the infected (informed) class is used as a strategy to
accelerate the spread of information. We formulate an optimal control problem
for optimizing a net reward function, a linear combination of the reward due to
information spread and cost due to application of controls. The time varying
resource allocation and seeds for the epidemic are jointly optimized. A problem
variation includes a fixed budget constraint. We prove the existence of a
solution for the optimal control problem, provide conditions for uniqueness of
the solution, and prove some structural results for the controls (e.g. controls
are non-increasing functions of time). The solution technique uses Pontryagin's
Maximum Principle and the forward-backward sweep algorithm (and its
modifications) for numerical computations. Our formulations lead to large
optimality systems with up to about 200 differential equations and allow us to
study the effect of network topology (Erdos-Renyi/scale-free) on the controls.
Results reveal that the allocation of campaigning resources to various degree
classes depends not only on the network topology but also on system parameters
such as cost/abundance of resources. The optimal strategies lead to significant
gains over heuristic strategies for various model parameters. Our modeling
approach assumes uncorrelated network, however, we find the approach useful for
real networks as well. This work is useful in product advertising, political
and crowdfunding campaigns in social networks.Comment: 14 + 4 pages, 11 figures. Author's version of the article accepted
for publication in IEEE/ACM Transactions on Networking. This version includes
4 pages of supplementary material containing proofs of theorems present in
the article. Published version can be accessed at
http://dx.doi.org/10.1109/TNET.2015.251254
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