With the estimated infection networks at hand, we applied the Equal Graph Partitioning (EGP) algorithm to remove the smallest sets of nodes that will efficiently fragment the estimated networks. We then immunized the same set of nodes on the actual infection network before simulating subsequent epidemics. We compared the effectiveness of the targeted strategy to an untargeted method that randomly isolates the same number of nodes, and showed that the former outperforms the latter in decreasing and delaying the peak of the epidemics, as well as reducing the total number of infections. We also applied the proposed strategy at different times after the epidemic has started and showed that it is still effective in decreasing the peak infection rate and total number of cases even when applied late into the epidemic. In particular, we demonstrated that the EGP based strategy is surprisingly effective in mitigating epidemics even when the estimated network is not very accurate. Through visualizing small network, we find that in spite of the large number of wrongly estimated links, the nodes appearing in the estimated network are concentrated along the backbones of the actual network and thus play important roles in the disease transmission.