Coverage problem is one of the fundamental issues in the design of wireless sensor network, which has a great impact on the performance of sensor network. In this article, coverage problem was investigated using a mathematical model named Birth-death process. In this model, sensor nodes joining into networks at every period of time is considered as the rebirth of network and the quitting of sensor nodes from the networks is considered as the death of the network. In the end, an analytical solution is used to investigate the appropriate rate to meet the coverage requirement . Coverage problem is one of the fundamental issues in the design of wireless sensor network, which has a great impact on the performance of sensor network. In this article, coverage problem was investigated using a mathematical model named Birth-death process. In this model, sensor nodes joining into networks at every period of time is considered as the rebirth of network and the quitting of sensor nodes from the networks is considered as the death of the network. In the end, an analytical solution is used to investigate the appropriate rate to meet the coverage requirement.