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Broadcast service is widely used during the life time of a wireless sensor network (WSN), such as networking setup, data collection/storage and query answering. In the past few years, many works have been done to improve its efficiency by reducing redundant broadcast messages. However, most of these works assume that all sensor nodes are active throughout a broadcast process and thus are difficult to be deployed in low duty-cycled WSNs, where sensor nodes switch between work and sleep to save energy and extend the network's life time. This problem is further aggravated by the difficulties to achieve global synchronization and rigid work-sleep schedules as the number of sensor nodes increases. To solve this problem, this paper remodels the broadcast problem to consider low duty-cycle and shows the lower bounds for time and message costs. We then propose an adaptive algorithm for dynamic message forwarding scheduling in this context, which enables a reliable and efficient broadcast service with low delay. Also, we demonstrate by extensive simulations that the proposed algorithm is not only robust against wireless communication loss but also performs close to optimal in terms of both time and message costs.