Optimal Resource Allocation for Control of Networked Epidemic Models
Cameron Nowzari, Victor M. Preciado, George Pappas

Citation
Cameron Nowzari, Victor M. Preciado, George Pappas. "Optimal Resource Allocation for Control of Networked Epidemic Models". IEEE Transactions on Control of Network Systems, 2015.

Abstract
This work proposes and analyzes a generalized epidemic model over arbitrary directed graphs with heterogeneous nodes. The proposed model, called the Generalized Susceptible-Exposed-Infected-Vigilant (G-SEIV), subsumes a large number of popular epidemic models considered in the literature as special cases. Using a mean-field approximation, we derive a set of ODEs describing the spreading dynamics, provide a careful analysis of the disease-free equilibrium, and derive necessary and sufficient conditions for global exponential stability. Building on this analysis, we consider the problem of containing an initial epidemic outbreak under budget constraints. More specifically, we consider a collection of control actions (e.g. administering vaccines/antidotes, limiting the traffic between cities, or running awareness campaigns), for which we are given suitable cost functions. In this context, we develop an optimization framework to provide solutions for the following two allocation problems: (i) find the minimum cost required to eradicate the disease at a desired exponential decay rate, and (ii) given a fixed budget, find the resource allocation to eradicate the disease at the fastest possible exponential decay rate. Our technical approach relies on the reformulation of these problems as geometric programs that can be solved efficiently in polynomial time using tools from graph theory and convex optimization. In contrast with previous works, our optimization framework allows us to simultaneously allocate different types of control resources over heterogeneous populations under budget constraints. We illustrate our results through numerical simulations.

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Citation formats

• HTML

  Cameron Nowzari, Victor M. Preciado, George Pappas. <a
  href="http://www.terraswarm.org/pubs/627.html"
  >Optimal Resource Allocation for Control of Networked
  Epidemic Models</a>, <i>IEEE Transactions on
  Control of Network Systems</i>,  2015.

• Plain text

  Cameron Nowzari, Victor M. Preciado, George Pappas.
  "Optimal Resource Allocation for Control of Networked
  Epidemic Models". <i>IEEE Transactions on Control
  of Network Systems</i>,  2015.

• BibTeX

  @article{NowzariPreciadoPappas15_OptimalResourceAllocationForControlOfNetworkedEpidemic,
      author = {Cameron Nowzari and Victor M. Preciado and George
                Pappas},
      title = {Optimal Resource Allocation for Control of
                Networked Epidemic Models},
      journal = {IEEE Transactions on Control of Network Systems},
      year = {2015},
      abstract = {This work proposes and analyzes a generalized
                epidemic model over arbitrary directed graphs with
                heterogeneous nodes. The proposed model, called
                the Generalized
                Susceptible-Exposed-Infected-Vigilant (G-SEIV),
                subsumes a large number of popular epidemic models
                considered in the literature as special cases.
                Using a mean-field approximation, we derive a set
                of ODEs describing the spreading dynamics, provide
                a careful analysis of the disease-free
                equilibrium, and derive necessary and sufficient
                conditions for global exponential stability.
                Building on this analysis, we consider the problem
                of containing an initial epidemic outbreak under
                budget constraints. More specifically, we consider
                a collection of control actions (e.g.
                administering vaccines/antidotes, limiting the
                traffic between cities, or running awareness
                campaigns), for which we are given suitable cost
                functions. In this context, we develop an
                optimization framework to provide solutions for
                the following two allocation problems: (i) find
                the minimum cost required to eradicate the disease
                at a desired exponential decay rate, and (ii)
                given a fixed budget, find the resource allocation
                to eradicate the disease at the fastest possible
                exponential decay rate. Our technical approach
                relies on the reformulation of these problems as
                geometric programs that can be solved efficiently
                in polynomial time using tools from graph theory
                and convex optimization. In contrast with previous
                works, our optimization framework allows us to
                simultaneously allocate different types of control
                resources over heterogeneous populations under
                budget constraints. We illustrate our results
                through numerical simulations.},
      URL = {http://terraswarm.org/pubs/627.html}
  }
  

Posted by Christopher Brooks on 29 Sep 2015.
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