SciCAM M.S. Thesis Defense: Graph Curvature for COVID-19 Network Risk Analytics

Speaker Name
Qingyuan Cui
Speaker Title
SciCAM M.S. Student
Speaker Organization
Scientific Computing and Applied Mathematics M.S.
Start Time
End Time
Location
Virtual Event

Join us on Zoom:  https://ucsc.zoom.us/j/92054074931?pwd=eWZOdzVVemphUkdvYUtOcnc5Wjg5QT09 - Passcode: 866950

Abstract: Curvature of a smooth manifold is both intuitive and has been studied in differential geometry for a long time. However, the notion of curvature for metric spaces in general, and for graphs in particular, is a relatively recent idea. In 2015, graph Ricci curvature was introduced as a framework to consider neighborhood to neighborhood interactions within a weighted undirected graph. In this thesis, we generalize graph Ricci curvature for weighted directed graphs, and apply this notion to analyze the spread of the Coronavirus disease 2019 (COVID-19) across the counties in the state of California.

We use real data for the daily traffic across different counties in California, and the daily COVID-19 case counts from March 2020 to March 2021. We demonstrate that graph Ricci curvature, and curvatures derived from it - such as graph scalar curvature - are particularly suited to dynamically predict and locate the onset and intensity of virus spread. The outcome of this thesis is a novel geometric data-driven risk analytics methodology to identify time-varying network-level risks for a virus spread. We envisage that our ideas will be useful for designing dynamic nonpharmaceutical intervention (NPI) strategies across the network to optimally mitigate the spread of the virus.

Graduate Program
Scientific Computing and Applied Mathematics M.S.