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Efficient data gathering is an important issue for wireless sensor networks with mobile sinks. However, high sink update cost causes sensor nodes to consume much energy, especially when sinks move frequently. This paper proposes two energy-efficient data gathering strategies in wireless sensor networks using a mobile sink. The sink moves based on improved Gauss-Markov mobility model (IGMM) and full coverage mobility model (FCM) in the surveillance region, and gathers interesting data. Since every node only communicates with sink and need not relay other data packets, the proposed strategies can efficiently reduce energy consumption and prolong the whole network lifetime. Simulation results and analysis show IGMM and FCM achieve good performance.