Predicting the sources of an outbreak with a spectral technique

Abstract

The epidemic spreading of a disease can be described by a contact network whose nodes are persons or centers of contagion and links heterogeneous relations among them. We provide a procedure to identify multiple sources of an outbreak or their closer neighbors. Our methodology is based on a simple spectral technique requiring only the knowledge of the undirected contact graph. The algorithm is tested on a variety of graphs collected from outbreaks including fluency, H5N1, Tbc, in urban and rural areas. Results show that the spectral technique is able to identify the source nodes if the graph approximates a tree sufficiently.

Inferring the origin of an epidemic with a dynamic message-passing algorithm

“…Information about the origin could be extremely useful to reduce or prevent future outbreaks. Whereas the dynamics and the prediction of epidemic spreading in networks have attracted a considerable number of works, for a review see [1][2][3], the problem of estimating the epidemic origin has been mathematically formulated only recently [4], followed by a burst of research on this practically important problem [5][6][7][8][9][10][11]. In order to make the estimation of the origin of spreading a well-defined problem we need to have some knowledge about the spreading mechanism.…”

“…Examples include the distance centrality or the Jordan center of a graph [4][5][6][7]. The problem was generalized to estimating a set of epidemic origins using spectral methods in [8,9]. Another line of approach uses more detailed information about the epidemic than just a snapshot at a given time [10].…”

Algorithmic advances in anonymous communication over networks

“…Most platforms store both messages and authorship information on centralized servers, which makes them vulnerable to government subpoenas, hacking, or direct company access, for the purpose of identifying the author of a message. Moreover, the spreading protocol used by existing platforms places users at risk of deanonymization against adversaries with side information, as proved in recent advances [31], [32], [33], [34], [35], [36]. Thus, even distributed architectures do not solve the problem.…”

Network observability and localization of the source of diffusion based on a subset of nodes

“…. , p all the possible p solutions of the original problem (4). Again, instead of solving the combinatorial problem (4), and searching for multiple solutions, we resort to solving the relaxed l 1 optimization problem (5).…”

“…Once the best source is found, a new source is calculated by removing the previously chosen source and solving again for a smaller infected graph. Multiple sources are also localized in [4], by identifying which nodes reduce the most the largest eigenvalue of the adjacency matrix after its removal. Through simulation, it is shown that the proposed technique is able to identify the source nodes if the graph approximates a tree sufficiently well.…”