D. Taylor, F. Klimm, H.A. Harrington, M. Kramar, K Mischaikow, M.A. Porter and P.J. Mucha, Topological data analysis of contagion maps for examining spreading processes on networks, Nature Communications 6, 7723,(2015).
In the last decades mechanism of spreading epidemics and ideas, around the world, has changed. Previously, they used to spread as a wave front across part of the earth surface. Now due to the presence of airline transportation or communication media, clusters of a contagion can suddenly appear in distant locations. We investigated how spreading of multiple contagions on a network can be used to understand properties of the underlying network, such as structure of the manifold on which the nodes of the network are embedded as well as structure of the long range connections. These insights could help improving the modeling, forecasting and control of spreading processes. The methods that we developed can be also used for dimension reduction and manifold learning. In the earlier work, we mainly concentrated on Watts threshold model. In our ongoing work we are trying to analyze dynamics of more complicated spreading models.