Title:
Mathematical Modeling of Cholera: Disease Invasion on Community Network

Abstract:
Consider a set of communities (patches), connected to one another according to a weighted digraph. When can a disease such as cholera invade this network? The answer to this question depends on both the network structure and the properties of the communities. In particular, the rooted spanning in-trees of the network and a generalization of the group inverse of the graph Laplacian play fundamental roles in determining the ability of disease to invade. This is joint work with J. Tien, M. Eisenberg, and P. van den Driessche.