The Bass diffusion model on networks with correlations and inhomogeneous advertising

M.L. Bertotti, J. Brunner and G. Modanese

Chaos, Solitons & Fractals, 2016, vol. 90, issue C, 55-63

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/kγ, where k=1,…,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 γ 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.

Keywords: Innovation diffusion; Bass equation; scale-free networks; correlated networks (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (7)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:90:y:2016:i:c:p:55-63

DOI: 10.1016/j.chaos.2016.02.039

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