We consider the spread of an infectious disease in a heterogeneous environment, modeled as a network of patches. We focus on the invasibility of the disease, as quantified by the basic reproduction number  , and investigate how geographic locations of disease hotspots and the changes in the network structure (e.g., due to human behavior) affect the value of . These effects can be characterized using new indices for the network average and network heterogeneity, providing both qualitative and quantitative information for mitigating disease spread.