Tracking Down an Epidemic’s Source (Physics 5, 89 (2012) | DOI: 10.1103/Physics.5.89)
From the post:
Epidemiologists often have to uncover the source of a disease outbreak with only limited information about who is infected. Mathematical models usually assume a complete dataset, but a team reporting in Physical Review Letters demonstrates how to find the source with very little data. Their technique is based on the principles used by telecommunication towers to pinpoint cell phone users, and they demonstrate its effectiveness with real data from a South African cholera outbreak. The system could also work with other kinds of networks to help governments locate contamination sources in water systems or find the leaders in a network of terrorist contacts.
A rumor can spread across a user network on Twitter, just as a disease spreads throughout a network of personal contacts. But there’s a big difference when it comes to tracking down the source: online social networks have volumes of time-stamped data, whereas epidemiologists usually have information from only a fraction of the infected individuals.
To address this problem, Pedro Pinto and his colleagues at the Swiss Federal Institute of Technology in Lausanne (EPFL) developed a model based on the standard network picture for epidemics. Individuals are imagined as points, or “nodes,” in a plane, connected by a network of lines. Each node has several lines connecting it to other nodes, and each node can be either infected or uninfected. In the team’s scenario, all nodes begin the process uninfected, and a single source node spreads the infection from neighbor to neighbor, with a random time delay for each transmission. Eventually, every node becomes infected and records both its time of infection and the identity of the infecting neighbor.
To trace back to the source using data from a fraction of the nodes, Pinto and his colleagues adapted methods used in wireless communications networks. When three or more base stations receive a signal from one cell phone, the system can measure the difference in the signal’s arrival time at each base station to triangulate a user’s position. Similarly, Pinto’s team combined the arrival times of the infection at a subset of “observer” nodes to find the source. But in the infection network, a given arrival time could correspond to multiple transmission paths, and the time from one transmission to the next varies randomly. To improve their chances of success, the team used the fact that the source had to be one of a finite set of nodes, unlike a cell phone user, who could have any of an infinite set of coordinates within the coverage area.
Summarizes: Locating the Source of Diffusion in Large-Scale Networks Pedro C. Pinto, Patrick Thiran, and Martin Vetterli Phys. Rev. Lett. 109, 068702 (2012).
One wonders if participation in multiple networks, some social, some electronic, some organizational, would be amenable to record linkage type techniques?
Leaks from government could be tracked using only one type of network but that is likely to be incomplete and misleading.