Rumor spreading with nonlinear infectivities in weighted networks

In the standard rumor spreading model, each node is treated equally and each link between two nodes, has the same weight. But in the real world, each node represents individuals. That means we should treat them respectively. So we introduce two weights for one link in the different parts during the spreading process. One is when an ignorant meets a spreader while the other is when a spreader encounters another spreader. Both of weights stand for the interaction between two connected nodes. We also analytically simulate the process of spreading rumors both on the small-world network and the scale-free network. First, we imitate the time evolution of three groups, namely, the ignorant, the spreader and the stifler. Second, we show the effects of parameters in the model.