Reconstructing Network Outbreaks under Group Surveillance

2026-02-11

AI Summary

This study addresses the problem of reconstructing epidemic transmission cascades from pooled surveillance data, such as wastewater or aerosol samples, under the independent cascade model. It introduces POOLCASCADEMLE, the first framework to incorporate group testing into network-based epidemic reconstruction, moving beyond the conventional assumption of individual-level testing. The method identifies the maximum-likelihood cascade subgraph consistent with observed positive pools by assigning at least one infection source to each positive pool. Leveraging the Group Steiner Tree problem, the authors design an approximation algorithm and develop a linear programming relaxation with rounding for the single-hop transmission scenario. Experiments on both real-world and synthetic contact networks demonstrate that the proposed approach significantly outperforms state-of-the-art baselines that rely on individual testing, achieving superior accuracy in infection source identification and prevalence estimation.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Content-based information diffusion

Abstract

A key public health problem during an outbreak is to reconstruct the disease cascade from a partial set of confirmed infections. This has been studied extensively under the Maximum Likelihood Estimation (MLE) formulation, which reduces the problem to finding some type of Steiner subgraph on a network. Group surveillance like wastewater or aerosol monitoring is a form of mass/pooled testing where samples from multiple individuals are pooled together and tested once for all. While a single negative test clears multiple individuals, a positive test does not reveal the infected individuals in the test pool. We introduce the POOLCASCADEMLE problem in the setting of a network propagation process, where the goal is to find a MLE cascade subgraph which is consistent with the pooled test outcomes. Previous work on reconstruction assumes that the test results are of individuals, i.e., pools of size one, and requires a consistent cascade to connect the positive testing nodes. In POOLCASCADEMLE, a consistent cascade must choose at least one node in each positive pool, adding another combinatorial layer. We show that, under the Independent Cascade (IC) model, POOLCASCADEMLE is NP-hard, and present an approximation algorithm based on a reduction to the Group Steiner Tree problem. We also consider a one-hop version of this problem, in which the disease can spread for one time step after being seeded. We show that even this restricted version is NP-hard, and develop a method using linear programming relaxation and rounding. We evaluate the performance of our methods on real and synthetic contact networks, in terms of missing infection recovery and prevalence estimation. We find that our approach outperforms meaningful baselines which correspond to pools of size one and use state-of-the-art methods.

Problem

• Network Outbreak Reconstruction
• Group Surveillance
• Pooled Testing
• Cascade Inference
• Epidemic Modeling

Innovation

• POOLCASCADEMLE
• Group Surveillance
• Network Cascade Reconstruction
• Group Steiner Tree
• Pooled Testing