Dynamic analysis of rumor spreading model for considering active network nodes and nonlinear spreading rate

Rumor spreading is an important form of social communication, and it will cause unnecessary panic and conflict to society. This paper aims to investigate the combined impact of the internal and external factors on the efficiency of rumor spreading over the social networks. In this paper, firstly, a modified ISR rumor spreading model on heterogeneous networks by taking into account the activity and infectivity of nodes and propagation environment was introduced. Then, through theoretical analysis, we derive the mean field equations with considering nonlinear spreading rate and active network nodes. Next, we calculate the basic reproduction number ℜ0 based on the next generation matrix method whose results reveal that if ℜ0<1, the rumor-free equilibrium is global asymptotically stable, the rumors will disappear. If ℜ0>1, the rumor-endemic equilibrium is global attractivity, then the number of spreaders will remain stable and the rumors will become endemic. Further, some numerical simulations are performed, which is consistent with the deterministic mean-field approach. Our results show that it is very important to consider the internal and external factors to control the spread of the rumors.