SICR rumor spreading model in complex networks: Counterattack and self-resistance

• We build two new rumor spreading models which consider the counterattack mechanism.
• We study the self-resistance feature of networks and its influence on rumor spreading.
• There do not exist rumor thresholds in the two new models.
• The final state of the rumor spreading process increases as self-resistance increases.
• The peak value of infective density decreases as self-resistance increases.

Rumor is an important form of social interaction. However, spreading of harmful rumors could have a significant negative impact on the well-being of the society. In this paper, considering the counterattack mechanism of the rumor spreading, we introduce two new models: Susceptible–Infective–Counterattack–Refractory (SICR) model and adjusted-SICR model. We then derive mean-field equations to describe their dynamics in homogeneous networks and conduct the steady-state analysis. We also introduce the self-resistance parameter ττ, and study the influence of this parameter on rumor spreading. Numerical simulations are performed to compare the SICR model with the SIR model and the adjusted-SICR model, respectively, and we investigate the spreading peak of the rumor and the final size of the rumor with various parameters. Simulation results are congruent exactly with the theoretical analysis. The experiment reveals some interesting patterns of rumor spreading involved with counterattack force.