演講者：虞沛鐸教授 ( 中原大學應用數學系 )

日   期：2025 年 05 月 28 日（星期三）13:30

地   點：國立高雄大學理學院 408 室

講   題：Mathematical and Computational Methods for Source Detection in SI Epidemic Models

摘   要：

Accurately detecting the origin of an epidemic or information outbreak in network structures is a fundamental challenge with applications for public health and infrastructure. This talk surveys two approaches to the source detection problem.

The first approach leverages graph centrality measures to identify likely sources, framing source detection as a combinatorial optimization problem on graphs. We review the concept of rumor (or epidemic) centrality, show how it emerges naturally from the maximum likelihood principle in discrete-time SI models, and present efficient message-passing algorithms and centrality-based heuristics. Empirical results on real-world SARS-CoV and COVID-19 contact tracing networks highlight the practical power of these algorithms.

The second approach extends source detection to continuous-time spreading models, where infection times along edges are governed by independent exponential distributions. Here, we incorporate both network structure and temporal information to improve accuracy. A probabilistic framework and a novel starlike tree approximation are introduced, providing tractable estimators for potential sources.

Finally, we discuss the computational challenge of evaluating epidemic centrality on large-scale networks and introduce a Markov Chain Monte Carlo (MCMC) framework. By employing weighted sampling and Metropolis-Hastings algorithms, we demonstrate scalable methods to approximate epidemic centrality efficiently.

The talk integrates these perspectives to provide both theoretical insights and practical algorithmic tools for the source detection problem, emphasizing their applicability to real-world networks.