Diffusion of New Products with Recovering Consumers

  title={Diffusion of New Products with Recovering Consumers},
  author={Gadi Fibich},
  journal={SIAM J. Appl. Math.},
  • G. Fibich
  • Published 6 January 2017
  • Business, Mathematics
  • SIAM J. Appl. Math.
We consider the diffusion of new products in the discrete Bass-SIR 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 “most-connected” configuration, where all consumers are interconnected (complete network), averaging over all consumers leads to an aggregate model, which combines the Bass model for… 

Figures from this paper

Diffusion of new products with heterogeneous consumers

This work analyzes the stochastic discrete Bass model to find that global dominance between two networks is not always preserved under “additive transformations”, such as adding an identical node to both networks.

Boundary Effects in the Discrete Bass Model

This work proves the main result that on a finite line, one-sided diffusion is strictly slower than two- sided diffusion (i.e., when each consumer can only be influenced by her left neighbor).

Modeling propagation of epidemics, social unrest and other collective behaviors

A family of Reaction-Diffusion systems introduced in [17] is concerned with unifying, generalizing, and enlarging the fields of application for epidemiology and collective behavior models and it is shown that this model can give rise to many diverse qualitative dynamics.

Exact description of SIR-Bass epidemics on 1D lattices

This paper is devoted to the study of a stochastic epidemiological model which is a variant of the SIR model to which we add an extra factor in the transition rate from susceptible to infected

Promotional Campaign Duration and Word-of-Mouth in Durable Good Adoption

Intensive promotional marketing campaigns can be used to introduce products to consumers with the goal of increasing awareness, consideration, purchase, and word-of-mouth (WOM). In this paper, we

About Correctness of Graph-Based Social Network Analysis

The author investigates unimodal networks with dyadic ties, provides several examples of correct and incorrect applications and recovers the roots of incorrectness.

Promotional Campaign Duration and Word-of-Mouth in Solar Panel Adoption

Intensive promotional marketing campaigns can be used to introduce products to consumers with the goal of increasing awareness, consideration, purchase, and word-of-mouth (WOM). In this paper, we



Bass-SIR model for diffusion of new products

The Bass-SIR model, which combines the Bass model for diffusion of new products with the SIR model for epidemics, is presented, in which clusters growth is limited by adopters' recovery and a small-worlds structure has a negligible effect on the diffusion.

The Diffusion of Microfinance

The results suggest that a model of diffusion can distinguish information passing from endorsement effects, and that understanding the nature of transmission may be important in identifying the ideal places to inject information.

Gossip: Identifying Central Individuals in a Social Network

It is shown that boundedly-rational individuals can, simply by tracking sources of gossip, identify those who are most central in a network according to "diffusion centrality," which nests other standard centrality measures.

Epidemiological modeling of online social network dynamics

The traditional SIR model of disease spread is modified by incorporating infectious recovery dynamics such that contact between a recovered and infected member of the population is required for recovery.

Using Complex Systems Analysis to Advance Marketing Theory Development

This study addresses two major issues facing current theory of innovation diffusion, and shows that notwithstanding some exceptions, the well-known Bass model performs well on aggregate data when the assumption that that all adopters have a possible equal effect on all other potential adopters is relaxed.

A New Product Growth for Model Consumer Durables

A growth model for the timing of initial purchase of new products is developed and tested empirically against data for eleven consumer durables, and a long-range forecast is developed for the sales of color television sets.

Emergence of scaling in random networks

A model based on these two ingredients reproduces the observed stationary scale-free distributions, which indicates that the development of large networks is governed by robust self-organizing phenomena that go beyond the particulars of the individual systems.

Collective dynamics of ‘small-world’ networks

Simple models of networks that can be tuned through this middle ground: regular networks ‘rewired’ to introduce increasing amounts of disorder are explored, finding that these systems can be highly clustered, like regular lattices, yet have small characteristic path lengths, like random graphs.

A contribution to the mathematical theory of epidemics

The present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.