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