Estimated homogeneous (left panel) and inhomogeneous (right panel) K-functions for Japanese encephalitis virus (JEV) outbreaks. The homogeneous K-function is not an appropriate fit due to the spatial dependency in JEV outbreaks as depicted by the divergent empirical (solid line) and theoretical functions (the latter is the theoretical function under complete spatial randomness, represented by the dashed line with confidence bands in grey). Conversely, the inhomogeneous K-function indicates that the model covariates sufficiently accounted for the spatial dependency (overlapping empirical and theoretical functions). The x-axes, r, represent increasing radii of subregions of the window of JEV outbreaks, while the y-axes represent the K-functions.