Effects of degree-biased transmission rate and nonlinear infectivity on rumor spreading in complex social networks

We introduce a generalized rumor spreading model and analytically investigate the spreading of rumors on scale-free (SF) networks. In the standard rumor spreading model, each node has an infectivity equal to its degree, and connectivity is uniform across all links. To generalize this model, we introduce an infectivity function that determines the number of simultaneous contacts that a given node (individual) may establish with its connected neighbors and a connectivity strength function (CSF) for the direct link between two connected nodes. These lead to a degree-biased propagation of rumors. For nonlinear functions, this generalization is reflected in the infectivity's exponent alpha and the CSF's exponent beta. We show that, by adjusting exponents alpha and beta, the epidemic threshold can be controlled. This feature is absent in the standard rumor spreading model. In addition, we obtain a critical threshold. We show that the critical threshold for our generalized model is greater than that of the standard model on a finite SF network. Theoretically, we show that beta = -1 leads to a maximum spreading of rumors, and computation results on different networks verify our theoretical prediction. Also, we show that a smaller alpha leads to a larger spreading of rumors. Our results are interesting since we obtain these results regardless of the network topology and configuration.