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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.