The key to the effective control of a diffusion system lies in how accurately we could predict its unfolding dynamics based on the observation of its current state. However, in the real-world applications, it is often infeasible to conduct a timely and yet comprehensive observation due to resource constraints. In view of such a practical challenge, the goal of this work is to develop a novel computational method for performing active observations, termed active surveillance, with limited resources. Specifically, we aim to predict the dynamics of a large spatio-temporal diffusion system based on the observations of some of its components. Towards this end, we introduce a novel measure, the γ value, that enables us to identify the key components by means of modeling a sentinel network with a row sparsity structure. Having obtained a theoretical understanding of the γ value, we design a backward-selection sentinel network mining algorithm (SNMA) for deriving the sentinel network via group sparse Bayesian learning. In order to be practically useful, we further address the issue of scalability in the computation of SNMA, and moreover, extend SNMA to the case of a non-linear dynamical system that could involve complex diffusion mechanisms. We show the effectiveness of SNMA by validating it using both synthetic datasets and five real-world datasets. The experimental results are appealing, which demonstrate that SNMA readily outperforms the state-of-the-art methods.