Bass-SIR model for diffusion of new products

TL;DR

This paper introduces the Bass-SIR model, a novel framework combining product adoption and epidemic spread dynamics, revealing that network structure has limited impact on diffusion in this model.

Contribution

The paper develops the Bass-SIR model, integrating the Bass and SIR models, and analyzes how network topology influences product diffusion.

Findings

Diffusion depends mainly on local network structure.

Small-world networks have negligible effect on diffusion.

Scale-free networks behave similarly to Cartesian networks.

Abstract

We consider the diffusion of new products in social networks, where consumers who adopt the product can later "recover" and stop influencing others to adopt the product. We show that the diffusion is not described by the SIR model, but rather by a novel model, the Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. The phase transition of consumers from non-adopters to adopters is described by a non-standard Kolmogorov-Johnson-Mehl-Avrami model, in which clusters growth is limited by adopters' recovery. Therefore, diffusion in the Bass-SIR model only depends on the local structure of the social network, but not on the average distance between consumers. Consequently, unlike the SIR model, a small-worlds structure has a negligible effect on the diffusion. Surprisingly, diffusion on scale-free networks is nearly identical to that on Cartesian ones.