Cooperative spreading dynamics on complex networks is a hot topic in the field of network science. In this paper, we propose a strategy to immunize some nodes based on their degrees. The immunized nodes disable the synergistic effect of cooperative spreading dynamics. We also develop a generalized percolation theory to study the final state of the spreading dynamics. By using the Monte Carlo method, numerical simulations reveal that immunizing nodes with a large degree cannot always be

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... l for containing cooperative spreading. For small values of transmission probability, immunizing hubs can suppress the spreading, while the opposite situation happens for large values of transmission probability. Furthermore, numerical simulations show that immunizing hubs increase the cost of the system. Finally, all numerical simulations can be well predicted by the generalized percolation theory.