Locating the source of diffusion in complex networks by time-reversal backward spreading

Abstract

Locating the source that triggers a dynamical process is a fundamental but challenging problem in complex networks, ranging from epidemic spreading in society and on the Internet to cancer metastasis in the human body. An accurate localization of the source is inherently limited by our ability to simultaneously access the information of all nodes in a large-scale complex network. This thus raises two critical questions: how do we locate the source from incomplete information and can we achieve full localization of sources at any possible location from a given set of observable nodes. Here we develop a time-reversal backward spreading algorithm to locate the source of a diffusion-like process efficiently and propose a general locatability condition. We test the algorithm by employing epidemic spreading and consensus dynamics as typical dynamical processes and apply it to the H1N1 pandemic in China. We find that the sources can be precisely located in arbitrary networks insofar as the locatability condition is assured. Our tools greatly improve our ability to locate the source of diffusion in complex networks based on limited accessibility of nodal information. Moreover, they have implications for controlling a variety of dynamical processes taking place on complex networks, such as inhibiting epidemics, slowing the spread of rumors, pollution control, and environmental protection.

On the Properties of Gromov Matrices and Their Applications in Network Inference

“…We apply the Gromov method (using convex combination), similar to the snapshot observation based estimation described above (we refer the reader to [21] for details). We compare the Gromov method with the BFS tree based approach (called BFS-MLE), as well as other approaches: GAU [10] and TRBS [33], on various networks. We use average error distance as well as 1%-accuracy as the evaluation metrics.…”

Estimating Infection Sources in Networks Using Partial Timestamps

“…The reference [30] proposed a sequential source estimation algorithm that allows online update of the source estimate as timestamps are observed sequentially. In [31], a time-reversal backward spreading (TRBS) algorithm was proposed to infer a single source in a weighted network. The papers [32], [33] discuss the selection of observer nodes under the deterministic slotted SI model, so as to achieve low probability of error detection.…”

Spreading predictability in complex networks

“…Spreading dynamics is an important issue in spreading and controlling [1][2][3] of 2 rumor [4][5][6][7] and disease [8][9][10][11], marketing [12], recommending [13][14][15], source 3 detecting [16,17], and many other interesting topics [18][19][20][21][22]. How to predict the 4 infection probability [23], infected scale [24,25], and even the infected nodes precisely 5 has been gotten much attention in recent years.…”

“…How to predict the 4 infection probability [23], infected scale [24,25], and even the infected nodes precisely 5 has been gotten much attention in recent years. 6 diverse collection of outbreaks and identified a fundamental entropy barrier for disease 16 time series forecasting through adopting permutation entropy as a model independent 17 measure of predictability. Funk et al [29] presented a stochastic semi-mechanistic 18 model of infectious disease dynamics that was used in real time during the 2013-2016 19 West African Ebola epidemic to fit the simulated trajectories in the Ebola Forecasting 20 Challenge, and to produce forecasts that were compared to following data points.…”