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In earlier rumor spreading models, at each time step nodes contact all oftheir neighbors. In more realistic scenario it is possible that a node maycontact only some of its neighbors to spread the rumor. Therefore it is must inreal world complex networks, the classic rumor spreading model need to bemodified to consider the dependence of rumor spread rate on the degree of thespreader and the informed nodes. We have given a modified rumor spreading modelto accommodate these facts. This new model, has been studied for rumorspreading in complex networks in this work. Nonlinear rumor spread exponent$\alpha$ and degree dependent tie strength exponent $\beta$ in any complexnetwork gives rumor threshold as some finite value. In the present work, themodified rumor spreading model has been studied in scale free networks. It isalso found that if $ \alpha $ and $ \beta $ parameters are tuned to appropriatevalue, the rumor threshold becomes independent of network size. In any socialnetwork, rumors can spread may have undesirable effect. One of the possiblesolutions to control rumor spread, is to inoculate a certain fraction of nodesagainst rumors. The inoculation can be done randomly or in a targeted fashion.We have used modified rumor spreading model over scale free networks toinvestigate the efficacy of inoculation. Random and targeted inoculationschemes have been applied. It has been observed that rumor threshold in randominoculation scheme is greater than the rumor threshold in the model without anyinoculation scheme. But random inoculation is not that much effective. Therumor threshold in targeted inoculation is very high than the rumor thresholdin the random inoculation in suppressing the rumor.

Nonlinear spread of rumor and inoculation strategies in the nodes with degree dependent tie strength in complex networks