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

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.