The reaction-diffusion (RD) equations in continuous space have made plentiful achievements in exploration of epidemiological patterns, but their spatiotemporal dynamics are limitedly supported in essence by the RD equations defined on a class of regular lattices as their counterparts discretized in space. However, patterns in complex spatial networks beyond lattices networks remain largely unexplored. In this talk, we creatively develop an epidemic reaction-diffusion model defined on our well-designed basic and modified spatially embedded networks to investigate the epidemiological patterns in spatial networks. We apply some basic properties of the Kronecker product to determine the eigenvalues and their corresponding eigenvectors of a high-dimensional matrix, which leads us to derive the necessary and sufficient conditions for Turing instability. With series and groups of comparative simulations, we systematically study the influence of factors including network size, nonlocal connectivity, asymmetrical connectivity, degree heterogeneity and random connected links on the pattern formations in spatial networks, and obtain some scarcely documented results deepening and broadening our understanding about the epidemiological patterns in space and networks.