### Monday, August 24, 2015 (3:15 p.m. in Yost 306)

**Title: **Disease Invasion on Community Networks

**Speaker:** Joe Tien (Assistant Professor, Ohio State University)

**Abstract: **Consider a set of communities (patches), connected to one another by a network. When can disease invade this network? This talk will consist of two parts relating to this question. In the first, I will show how the ability of disease to invade depends both upon the properties of the communities, as well as on the network structure. In particular, this dependence can be made explicit for a broad class of disease models, through the rooted spanning trees of the network and a generalization of the graph Laplacian. This first part is joint work with Zhisheng Shuai, Marisa Eisenberg, and Pauline van den Driessche. In the second part, I will discuss how network structure for graphs with “decay” can be described in terms of this generalized inverse. This generalized inverse is connected to transient random walks on the graph, and can be used to derive a natural distance metric, centrality measures, and community detection algorithms. I will describe some of these measures, together with implications for disease dynamics. This second part is joint work with Karly Jacobsen.