We investigate the spread of diseases, computer viruses or information oncomplex networks and also immunization strategies to prevent or control thespread. When an entire population cannot be immunized and the effect ofimmunization is not perfect, we need the targeted immunization withimmunization rate. Under such a circumstance we calculate epidemic thresholdsfor the SIR and SIS epidemic models. It is shown that, in scale-free networks,the targeted immunization is effective only if the immunization rate is equalto one. We analyze here epidemic spreading on directed complex networks, butsimilar results are also valid for undirected ones.
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