Controlling recurrent infectious diseases is a vital yet complicated problem. In this paper, we propose a novel active screening model (ACTS) and algorithms to facilitate active screening for recurrent diseases (no permanent immunity) under infection uncertainty. Our contributions are: (1) A new approach to modeling multi-round network-based screening/contact tracing under uncertainty, which is a common real-life practice in a variety of diseases; (2) Two novel algorithms, Full- and Fast-REMEDY. Full-REMEDY considers the effect of future actions and finds a policy that provides high solution quality, where Fast-REMEDY scales linearly in the size of the network; (3) We evaluate Full- and Fast-REMEDY on several real-world datasets which emulate human contact and find that they control diseases better than the baselines. To the best of our knowledge, this is the first work on multi-round active screening with uncertainty for diseases with no permanent immunity.