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

Graham Kesler O'Connor¹, Julia M Jess¹, Devlin Costello¹

¹Department of Applied Mathematics, University of Colorado, Boulder, CO, 80309-0526, US.

Bulletin of Mathematical Biology

|April 26, 2026

Summary

This summary is machine-generated.

Identifying infection origins in tree networks is challenging. This study shows a limited number of infection observations can statistically pinpoint the outbreak source using Laplace transforms and scale-invariant estimators.

Keywords:

Diffusion source Graph Infection propagation Information diffusion Laplace estimation Rumor spreading SI model

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Area of Science:

Epidemiology
Network Science
Statistical Modeling

Background:

Outbreaks in networks pose challenges for source localization.
Understanding infection spread dynamics is crucial for containment.
Observing all infection events is often impractical.

Purpose of the Study:

To develop methods for localizing infection sources in tree-structured networks.
To determine if a subset of observed infection times is sufficient for source identification.
To propose novel statistical estimators for source localization.

Main Methods:

Utilizing a susceptible-infected outbreak model on tree networks.
Modeling infection propagation with random edge-delays.
Employing joint Laplace transforms of observed infection times.
Developing scale-invariant estimators based on explicit transform forms.

Main Results:

Demonstrated that a reduced set of observers can statistically identify the infection source.
Characterized source identifiability using joint Laplace transforms.
Proposed and validated scale-invariant estimators.
Achieved accurate localization on synthetic and real-world (river) networks.

Conclusions:

Source localization is feasible even with limited infection data in tree networks.
Laplace transforms provide a powerful tool for analyzing infection spread and identifiability.
The proposed estimators offer a robust approach for identifying outbreak origins in various network structures.