A study on the interaction between two rumors in homogeneous complex networks under symmetric conditions

•Two rumors may have positive or negative impact on each other’s spreading.•A nine-state rumor interaction model in homogeneous complex network is proposed.•Spreading properties are obtained by numerical solution of mean-field equations.•Interactions between two rumors lead to the variation of spreading properties.

The propagating dynamics of more than one rumor has received a substantial amount of attention in recent years. To investigate the effects of interactions between two rumors under symmetric conditions, we built a model based on an ordinary differential equation system while assuming that each individual’s spreading rate after receiving one rumor depends on whether he/she knows the other rumor. In certain cases, two rumors accelerate the spread of each other, while in a portion of the other cases they impede or decelerate the spread of each other. We discuss these effects by dividing the total population into nine groups that correspond to nine states, and we subsequently build the mean-field equations for the two-rumor interaction based on the SIR model in a homogeneous complex network, and we find their numerical solution with varying interaction factors for the rates of spreading and becoming disinterested. The results show that when we change these interaction factors, the density curves of the nine states and their maximum values will change accordingly by a series of rules, which demonstrates the corresponding effects when there is a positive or negative interaction between the two rumors. Our work could establish a foundation for further study of this issue.