A key characteristic of the spread of infectious diseases is their ability to use efficient transmission paths within contact graphs. This enables the pathogen to maximise infection rates and spread within a target population. In this work, we devise techniques to localise infections and decrease infection rates based on a principled analysis of disease transmission paths within human-contact networks (proximity graphs). Experimental results of disease spreading shows that that at low visibility rates contact tracing slows disease spreading. However to stop disease spreading, contact tracing requires both significant visibility (at least 60%) into the proximity graph and the ability to place half of the population under isolation. We find that pro-actively isolating super-links -- key proximity encounters -- has significant benefits: targeted isolation of a fourth of the population based on 35% visibility into the proximity graph prevents an epidemic outbreak. It turns out that isolating super-spreaders is more effective than contact tracing and testing but less effective than targeting super-links. We highlight the important role of topology in epidemic outbreaks. We argue that proactive innoculation of a population by disabling super-links and super-spreaders may have an important complimentary role alongside contact tracing and testing as part of a sophisticated public-health response to epidemic outbreaks.