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Wireless sensor networks have been widely studied in various applications such as environmental monitoring, battlefield surveillance, and intrusion detection recently. One of the important applications is to detect mobile targets (e.g., invaders) by using mobile sensor nodes. Consider a closed region where there are several mobile sensors patrolling and trying to capture targets who are able to sense their environments and then plan their movements to avoid detection. The focuses of this paper are (a) to figure out a better movement strategy for a sensor for coping with the issue of detecting mobile targets with the deadline, and (b) to investigate the trade-off between the number of mobile sensors and the quality of detection represented by the detection probability before a given deadline. With the help of the proposed model, we design a detection strategy, called Single-hop Presence-aware Detection Strategy, to effectively capture the mobile target. The simulation results show that the model can predict the expected detection time precisely, and the number of sensors obtained from the model is adequate to satisfy the desired quality of detection.