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The Bass diffusion model on networks with correlations and inhomogeneous advertising

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

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.

Suggested Citation

  • Bertotti, M.L. & Brunner, J. & Modanese, G., 2016. "The Bass diffusion model on networks with correlations and inhomogeneous advertising," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 55-63.
  • Handle: RePEc:eee:chsofr:v:90:y:2016:i:c:p:55-63
    DOI: 10.1016/j.chaos.2016.02.039
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    References listed on IDEAS

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    1. Edmund Phelps, 2015. "Mass Flourishing: How Grassroots Innovation Created Jobs, Challenge, and Change," Economics Books, Princeton University Press, edition 1, number 10058-2.
    2. Frank M. Bass, 1969. "A New Product Growth for Model Consumer Durables," Management Science, INFORMS, vol. 15(5), pages 215-227, January.
    3. Hazhir Rahmandad & John Sterman, 2008. "Heterogeneity and Network Structure in the Dynamics of Diffusion: Comparing Agent-Based and Differential Equation Models," Management Science, INFORMS, vol. 54(5), pages 998-1014, May.
    4. Meade, Nigel & Islam, Towhidul, 2006. "Modelling and forecasting the diffusion of innovation - A 25-year review," International Journal of Forecasting, Elsevier, vol. 22(3), pages 519-545.
    5. Duncan J. Watts & Peter Sheridan Dodds, 2007. "Influentials, Networks, and Public Opinion Formation," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 34(4), pages 441-458, May.
    6. Eric Abrahamson & Lori Rosenkopf, 1997. "Social Network Effects on the Extent of Innovation Diffusion: A Computer Simulation," Organization Science, INFORMS, vol. 8(3), pages 289-309, June.
    7. T. Di Matteo & T. Aste & M. Gallegati, 2005. "Innovation flow through social networks: productivity distribution in France and Italy," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 47(3), pages 459-466, October.
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    Cited by:

    1. Carbone, Anna & Jensen, Meiko & Sato, Aki-Hiro, 2016. "Challenges in data science: a complex systems perspective," Chaos, Solitons & Fractals, Elsevier, vol. 90(C), pages 1-7.
    2. Laura Di Lucchio & Giovanni Modanese, 2024. "Generation of Scale-Free Assortative Networks via Newman Rewiring for Simulation of Diffusion Phenomena," Stats, MDPI, vol. 7(1), pages 1-15, February.
    3. Giovanni Modanese, 2023. "The Network Bass Model with Behavioral Compartments," Stats, MDPI, vol. 6(2), pages 1-13, March.
    4. M. L. Bertotti & G. Modanese, 2019. "The Bass Diffusion Model on Finite Barabasi-Albert Networks," Complexity, Hindawi, vol. 2019, pages 1-12, April.
    5. Azadeh Ahkamiraad & Yong Wang, 2018. "An Agent-Based Model for Zip-Code Level Diffusion of Electric Vehicles and Electricity Consumption in New York City," Energies, MDPI, vol. 11(3), pages 1-17, March.
    6. Koundre Aime Dieudonné Bah, 2024. "Assessing the Potential of Digital Tools to Enhance Transparency and Traceability in The Cocoa Value Chain in Ivory Coast," International Journal of Research and Innovation in Social Science, International Journal of Research and Innovation in Social Science (IJRISS), vol. 8(3), pages 2751-2780, March.

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