Bass-SIR model for diffusion of new products

摘要

We consider the diffusion of new products in social networks, where consumerswho adopt the product can later "recover" and stop influencing others to adoptthe product. We show that the diffusion is not described by the SIR model, butrather by a novel model, the Bass-SIR model, which combines the Bass model fordiffusion of new products with the SIR model for epidemics. The phasetransition of consumers from non-adopters to adopters is described by anon-standard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth islimited by adopters' recovery. Therefore, diffusion in the Bass-SIR model onlydepends on the local structure of the social network, but not on the averagedistance between consumers. Consequently, unlike the SIR model, a small-worldsstructure has a negligible effect on the diffusion. Surprisingly, diffusion onscale-free networks is nearly identical to that on Cartesian ones.