The independent spreaders involved SIR Rumor model in complex networks

• Independent spreaders involved SIR model is established and mean-field equations are derived.
• The global rumor popularity is considered in the model.
• The diffusion process and steady state is greatly influenced by independent spreaders.

Recent studies of rumor or information diffusion process in complex networks show that in contrast to traditional comprehension, individuals who participate in rumor spreading within one network do not always get the rumor from their neighbors. They can obtain the rumor from different sources like online social networks and then publish it on their personal sites. In our paper, we discuss this phenomenon in complex networks by adopting the concept of independent spreaders. Rather than getting the rumor from neighbors, independent spreaders learn it from other channels. We further develop the classic “ignorant-spreaders-stiflers” or SIR model of rumor diffusion process in complex networks. A steady-state analysis is conducted to investigate the final spectrum of the rumor spreading under various spreading rate, stifling rate, density of independent spreaders and average degree of the network. Results show that independent spreaders effectively enhance the rumor diffusion process, by delivering the rumor to regions far away from the current rumor infected regions. And though the rumor spreading process in SF networks is faster than that in ER networks, the final size of rumor spreading in ER networks is larger than that in SF networks.