Information Source Detection in the SIR Model: A Sample-Path-Based Approach

Abstract

This paper studies the problem of detecting the information source in a network in which the spread of information follows the popular Susceptible-Infected-Recovered (SIR) model. We assume all nodes in the network are in the susceptible state initially, except one single information source that is in the infected state. Susceptible nodes may then be infected by infected nodes, and infected nodes may recover and will not be infected again after recovery. Given a snapshot of the network, from which we know the graph topology and all infected nodes but cannot distinguish susceptible nodes and recovered nodes, the problem is to find the information source based on the snapshot and the network topology. We develop a sample-path-based approach where the estimator of the information source is chosen to be the root node associated with the sample path that most likely leads to the observed snapshot. We prove for infinite-trees, the estimator is a node that minimizes the maximum distance to the infected nodes. A reverse-infection algorithm is proposed to find such an estimator in general graphs. We prove that for -regular trees such that , where is the node degree and is the infection probability, the estimator is within a constant distance from the actual source with a high probability, independent of the number of infected nodes and the time the snapshot is taken. Our simulation results show that for tree networks, the estimator produced by the reverse-infection algorithm is closer to the actual source than the one identified by the closeness centrality heuristic. We then further evaluate the performance of the reverse infection algorithm on several real-world networks.Index Terms-Information source detection, sample-path-based approach, Susceptible-Infected-Recovered (SIR) model.

Identification of Patient Zero in Static and Temporal Networks: Robustness and Limitations

“…The second motivation comes from silent spreading of a certain class of computer viruses and worms through computer networks which become active simultaneously on a specific date. Unlike other approaches [12][13][14][15][16][17][18][19][20][21], we identified different source detectability regimes and our methodology is applicable to arbitrary network structures, and is limited solely by the ability to computationally produce realizations of the particular contagion process.…”

“…Due to its practical aspects and theoretical importance, the epidemic source detection problem on contact networks has recently gained a lot of attention in the complex network science community. This has led to the development of many different source detection estimators for static networks, which vary in their assumptions on the network structure (locally tree-like) or on the spreading process compartmental models (SI, SIR) [12][13][14][15][16][17][18][19][20][21] or both.…”

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.…”

“…The methods that have been studied in the existing works are mostly based on various kinds of graph-centrality measures. 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].…”

Back To The Source

“…An alternate line of work that also uses Assumption (B.1), allows the observed states to be noisy, i.e., potentially inaccurate. For example, a model in which it is not possible to distinguish between susceptible and recovered nodes was studied by Zhu et al [39].…”