Observer-Based Source Localization in Tree Infection Networks via Laplace Transforms

by Graham Kesler O’Connor, Julia M. Jess, Devlin Costello, Manuel E. Lladser

Pinpointing "patient zero" in an outbreak, whether a biological disease, a computer virus, or rumor is notoriously difficult. Our paper introduces two new statistical methods based on Laplace transforms to trace the origin of an infection in tree networks when only a subset of nodes report their infection times. This makes our methods suitable for any situation in which a susceptible-infected (SI) infection spreads through a network without loops, with infected nodes infecting susceptible neighbors after random, independent delays, with explicit Laplace transforms. In particular, our methods provide public health, cybersecurity, and intelligence officials with a general tool for tracing and containing outbreaks.

Middle: Formulation of the observers' infection times using Laplace transforms of the edge delays, alongside a proposed source estimator derived from the empirical Laplace transform of the observers. Left: Source localization on a linear network with node 0 as the sole observer, as the infection source shifts from node 1 to node 10. Right: Source localization performance along the Thukela River basin, where the leftmost node is the true source, estimated using the simulated infection times of three downstream observers selected at random.