How do networks shape the spread of disease and gossip?

A new approach to exploring the spread of contagious diseases or the latest celebrity gossip has been tested using London's street and underground networks. Results from the new approach could help to predict when a contagion will spread through space as a simple wave (as in the Black Death) and when long-range connections, such as air travel, enable it to seemingly jump over long distances and emerge in locations far from an initial outbreak. A team of mathematicians from Oxford University, University of North Carolina at Chapel Hill, and Rutgers University used a set of mathematical rules to encode how a contagion spreads, and then studied the outcomes of these rules. The researchers explored how disease or gossip might spread through London's transit network. Specifically, they illustrated how the street network overlaid with the London Underground network enables contagions to hop to a distant location. To analyse the behaviour of a contagion, the researchers drew on ideas from 'topology', a branch of mathematics used to characterise the structure of complex shapes. By studying the 'shape' of the data that results from a contagion, it is possible to distinguish between contagions that take long-distance hops across a network and those that exhibit a local (and slower) wave-like spreading pattern.