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This paper addresses the problem of sweep-based persistent surveillance (SBPS) using multiple Unmanned Aerial Vehicles (UAVs). Due to the variation of priority distributed in the area under surveillance, a novel concept of level-of-interest (LoI) is introduced to represent the relative priorities of the target areas. Inspired by an “age”- related algorithm in literature, we develop a novel recursive scheme with the LoI consideration. The algorithms on both single UAV case and multiple UAVs case are developed to decide the optimal target-choice based on the age-based performance index. The potential benefits of the proposed algorithms are demonstrated by simulations in both single UAV cases and multiple UAVs cases.