# Problems in Function Theory with Applications in Epidemic Modeling

Understanding the dynamics of epidemic spreading over graphs has attracted a substantial research attention recently. Researchers seek to find the role of the graph topology on the epidemic spreading. However, there are still many open problems on this topic. One important problem is to develop topological measures to quantify graphs with respect to epidemic spreading. This team has developed epidemic quasimetric, a measure that resembles effective resistance with low computational complexity and direct application to epidemic spreading and graph clustering. We are also working on epidemic spreading over graphs, particularly from spectral viewpoints. Here, we propose to extend the concept of epidemic quasimetric to study epidemic spreading over different spreading scenarios.

*Supported by National Science Foundation under Award DMS-1201427.* Any opinions, findings, and conclusions or recommendations expressed in this website are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.