Fractional Immunization in Hospital-transfer Graphs

How to control the spread of diseases over a network, given limited resources (like, eg., anti-bacterial chemicals)? The extra complication is that the resource provides only partial protection, slowing down the virus propagation speed, but not stopping it completely. Just such is the case of the spread of highly resistant bacteria in the inter-hospital patient transfer network. We examine exactly this problem in this paper; our contributions are: (a) we formulate and propose the problem as an optimization problem of how to best distribute resources to reduce the largest eigenvalue of the resultant adjacency matrix of the hospital-transfer network (b) we prove the problem is NP-complete and then propose near-optimal linear-time algorithms and finally, (c) we demonstrate the efficiency and accuracy of our algorithm compared to several other methods after extensive experiments on real-world datasets including US-MEDICARE and state-level interhospital patient transfer data. To the best of our knowledge, we are the first to formulate the problem, use truly nation-scale network data and principally propose effective algorithms. We found that targeting resources to a small subset of nodes using our algorithm was upto 6 times more effective than distributing infection-control resources uniformly, contrasting with current practice.