In this paper, we deal with the economic operation of a data backup scheme for various computer systems under disastrous information threats. To this end, we introduce a queueing model that combines disasters and two-stage queues. Making use of the matrix-geometric approach, we obtain its steady-state probabilities. From these results, we compute the average total cost with a recovery cost and a backup cost taken into account. With sample numerical results, we investigate the optimal backup operation that minimizes the average total cost.