The spread of rumors on complex networks has attracted wide attention in the field of management. In this paper, the generalized rumor spreading model is modified to take into account the vital of the spreader and the tie strength for the pairwise contacts between nodes in complex networks at degree-dependent spreading rate. Concretely, we introduce the infectivity exponent [Formula: see text], and the degree influenced real exponent [Formula: see text] into the analytical rumor spreading model. Rumor infectivity, [Formula: see text], where [Formula: see text], defines that each spreader node may contact [Formula: see text] neighbors within one time step. The tie strength between two nodes with degrees [Formula: see text] and [Formula: see text] are measured by [Formula: see text], [Formula: see text] is the degree influenced real exponent which depends on the type of complex networks and [Formula: see text] is a positive quantity. We use a tuning parameter [Formula: see text] to combine both the effect of the vital nodes and the strength of connectivity between nodes. We use analytical and numerical solutions to examine the threshold behavior and dynamics of the model on several models of social network. It was found that the infectivity exponent [Formula: see text], the degree influenced real exponent [Formula: see text] and tuning parameter [Formula: see text] affect the rumor threshold, one can adjust the parameters to control the rumor threshold which is absent for the standard rumor spreading model.
Steady-State Analysis of SECIR Rumor Spreading Model in Complex Networks