Fractional immunization in networks

Preventing contagion in networks is an important problem in public health and other domains. Targeting nodes to immunize based on their network interactions has been shown to be far more effective at stemming infection spread than immunizing random subsets of nodes. However, the assumption that selected nodes can be rendered completely immune does not hold for infections for which there is no vaccination or effective treatment. Instead, one can confer fractional immunity to some nodes by allocating variable amounts of infection-prevention resource to them. We formulate the problem to distribute a fixed amount of resource across nodes in a network such that the infection rate is minimized, prove that it is NP-complete and derive a highly effective and efficient linear-time algorithm. We demonstrate the efficiency and accuracy of our algorithm compared to several other methods using simulation on realworld network datasets including US-MEDICARE and state-level interhospital patient transfer data. We find that concentrating resources at a small subset of nodes using our algorithm is up to 6 times more effective than distributing them uniformly (as is current practice) or using network-based heuristics. To the best of our knowledge, we are the first to formulate the problem, use truly nation-scale network data and propose effective algorithms.