Finding Patient Zero via Low-Dimensional Geometric Embeddings

Researchers Stefan Huber and Dominik Kaaser have developed a novel geometric approach to solving the critical epidemiological challenge of identifying 'Patient Zero'—the original source of an infection. Their method, detailed in the arXiv preprint 'Finding Patient Zero via Low-Dimensional Geometric Embeddings,' leverages computational geometry techniques to embed complex contact networks into low-dimensional Euclidean spaces using Johnson-Lindenstrauss projections. This compression allows the system to operate on significantly reduced data while maintaining the structural relationships essential for accurate source detection.

In their proposed framework, once the network is embedded, the infection source is estimated as the network node closest to the center of gravity of all known infected nodes. This geometric intuition transforms a complex combinatorial search problem into a more tractable spatial computation. The researchers validated their estimator through simulations on Erdős-Rényi random graphs, demonstrating that it achieves 'meaningful reconstruction accuracy' despite the inherent information loss from dimensionality reduction.

The work sits at the intersection of computational geometry (cs.CG) and social/information networks (cs.SI), offering a fresh perspective on epidemic modeling within the independent cascade framework. By reducing the computational and data storage burden, this approach could enable faster, more scalable outbreak source identification in real-world scenarios where complete contact tracing data is unavailable or too massive to process with conventional methods.