The Bass diffusion model on networks with correlations and inhomogeneous advertising

TL;DR

This paper extends the Bass diffusion model by incorporating network structures with correlations and inhomogeneous advertising, revealing how network topology influences adoption dynamics and forecasting potential.

Contribution

It introduces a network-based version of the Bass model, analyzing the effects of correlations and targeted advertising on innovation diffusion.

Findings

Adoption peaks earlier in networks with few hubs and high connectivity.

Hubs' adoption curves predict overall adoption trends.

Targeted advertising on hubs can influence diffusion timing.

Abstract

The Bass model, which is an effective forecasting tool for innovation diffusion based on large collections of empirical data, assumes an homogeneous diffusion process. We introduce a network structure into this model and we investigate numerically the dynamics in the case of networks with link density $P(k)=c/k^\gamma$, where $k=1, \ldots , N$. The resulting curve of the total adoptions in time is qualitatively similar to the homogeneous Bass curve corresponding to a case with the same average number of connections. The peak of the adoptions, however, tends to occur earlier, particularly when $\gamma$ and $N$ are large (i.e., when there are few hubs with a large maximum number of connections). Most interestingly, the adoption curve of the hubs anticipates the total adoption curve in a predictable way, with peak times which can be, for instance when $N=100$, between 10% and 60% of the total adoptions peak. This may allow to monitor the hubs for forecasting purposes. We also consider the case of networks with assortative and disassortative correlations and a case of inhomogeneous advertising where the publicity terms are "targeted" on the hubs while maintaining their total cost constant.