We introduce a new quantity known as the network heterogeneity index, denoted by \(\mathcal {H}\) , to facilitate the investigation of disease propagation and population persistence in heterogeneous environments. Our mathematical analysis reveals that this index embodies the structure of such networks, the disease or population dynamics of patches, and the dispersal between patches. We present multiple representations of the network heterogeneity index and demonstrate that \(\mathcal {H} \ge 0\) . Moreover, we explore the applications of \(\mathcal {H}\) in epidemiology and ecology across various heterogeneous environments, highlighting its effectiveness in determining disease invasibility and population persistence.
