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

In the classic rumor spreading model, also known as susceptible-infectedremoved (SIR) model in which rumor spread out of each node proportionally to its degree and all edges have uniform tie strength between nodes. The rumor spread phenomenon is similar as epidemic spread, in which all the informed nodes spread rumor by informing their neighbor nodes. 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. Rumor spreads nonlinearly by pairwise contacts between nodes in complex networks at degree dependent spreading rate. Nonlinear rumor spread exponent α and degree dependent tie strength of nodes affect the rumor threshold. The degree exponent tie strength between two nodes is (kikj) β, where ki and kj are degrees of node i and j and β is tie strength exponent. By using the above two exponents 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 has been found to have a greater threshold than with previous classic rumor spreading model. It is also found that if α and β 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 1 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. It has also been observed that targeted inoculation scheme is more successful to stop the rumor in this model based on scale free networks. The proposed hypothesis is also verified by simulation results.