Identifying multiple infection sources in a network

Estimating which nodes are the infection sources that introduce a virus or rumor into a network, or the locations of pollutant sources, plays a critical role in limiting the potential damage to the network through timely quarantine of the sources. In this paper, we derive estimators for the infection sources and their infection regions based on the infection network geometry. We show that in a geometric tree with at most two sources, our estimator identifies these sources with probability going to one as the number of infected nodes increases. We extend and generalize our methods to general graphs, where the number of infection sources are unknown and there may be multiple sources. Numerical results are presented to verify the performance of our proposed algorithms under different types of graph structures.