  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.
