Diffusion of new products with recovering consumers
Abstract
We consider the diffusion of new products in the discrete BassSIR model, in which consumers who adopt the product can later "recover" and stop influencing their peers to adopt the product. To gain insight into the effect of the social network structure on the diffusion, we focus on two extreme cases. In the "mostconnected" configuration where all consumers are interconnected (complete network), averaging over all consumers leads to an aggregate model, which combines the Bass model for diffusion of new products with the SIR model for epidemics. In the "leastconnected" configuration where consumers are arranged on a circle and each consumer can only be influenced by his left neighbor (onesided 1D network), averaging over all consumers leads to a different aggregate model which is linear, and can be solved explicitly. We conjecture that for any other network, the diffusion is bounded from below and from above by that on a onesided 1D network and on a complete network, respectively. When consumers are arranged on a circle and each consumer can be influenced by his left and right neighbors (twosided 1D network), the diffusion is strictly faster than on a onesided 1D network. This is different from the case of nonrecovering adopters, where the diffusion on onesided and on twosided 1D networks is identical. We also propose a nonlinear model for recoveries, and show that consumers' heterogeneity has a negligible effect on the aggregate diffusion.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.01669
 Bibcode:
 2017arXiv170101669F
 Keywords:

 Physics  Physics and Society;
 Computer Science  Social and Information Networks