Consider a set of communities (patches), connected to one another by a network. When can disease invade this network? Intuitively, this should depend upon both the properties of the communities, as well as on the network structure. Here we make this dependence explicit for a broad class of disease models with environmental pathogen movement. In particular, the rooted spanning 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 Z. Shuai, M. Eisenberg, and P. van den Driessche.