A rumor spreading pairwise model on weighted networks. (English) Zbl 1484.91347
This paper studies a pairwise model on weighted networks to model the dynamics of a rumor in social networks. The rumor propagation is based on the SIR model, where S means spreader, I means ignorant and R means stifler. When a spreader meets an ignorant through an edge of weight \(w_i\), the ignorant agent becomes a spreader a rate \(\beta_i\), which relies on the edge weight per se. When a spreader meets a different spreader or a stifler, the first spreader becomes a stifler at a stifling rate \(\delta_i\) depending on the edge weight per se. Furthermore, it is assumed that a spreader becomes a stifler spontaneously at a rate \(\gamma\) due to forgetfulness. With this model, the basic reproductive ratio is derived as \(k\langle \beta\rangle^2/(\langle\beta^2 \rangle+\gamma\langle\beta\rangle)\), where \(k\) is the degree and \(\langle\beta\rangle\) is the average transmission rate over the network. Some numerical results are presented to illustrate the theoretic results under different scenarios.
Reviewer: Yilun Shang (Newcastle)
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