Rumor dynamics with inoculations for correlated scale free networks

We study the rumor spreading dynamics in complex networks, where degree correlations between the pair of nodes exist. An analytical description is provided that includes two vertices, degree-degree correlations in the dynamical evolution of the rumor spreading. In any social network, rumors can spread and may have undesirable effect. To control rumor spread, a certain fraction of nodes are inoculated against rumors. In this paper, the inoculation of nodes are done by random and targeted fashion with the variation of assortative coefficient in scale free networks. The new degree distributions of scale free networks have been calculated for both kind of inoculations. It has been observed that rumor threshold in targeted inoculation scheme is greater than the rumor threshold in the random inoculation scheme. In targeted inoculation scheme, rumor threshold for correlated networks is found to be smaller than in uncorrelated networks. Random inoculation is not that much effective for scale free networks. It is found that degree-degree correlation between nodes doesn't play any role in random inoculations. However, it is not true for targeted inoculation. The proposed hypothesis has also been verified by the simulation results.