1932

Abstract

Innovation diffusion processes have attracted considerable research attention for their interdisciplinary character, which combines theories and concepts from disciplines such as mathematics, physics, statistics, social sciences, marketing, economics, and technological forecasting. The formal representation of innovation diffusion processes historically used epidemic models borrowed from biology, departing from the logistic equation, under the hypothesis that an innovation spreads in a social system through communication between people like an epidemic through contagion. This review integrates basic innovation diffusion models built upon the Bass model, primarily from the marketing literature, with a number of ideas from the epidemiological literature in order to offer a different perspective on innovation diffusion by focusing on critical diffusions, which are key for the progress of human communities. The article analyzes three key issues: barriers to diffusion, centrality of word-of-mouth, and the management of policy interventions to assist beneficial diffusions and to prevent harmful ones. We focus on deterministic innovation diffusion models described by ordinary differential equations.

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2023-03-09
2024-04-30
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Literature Cited

  1. Abramson G, Zanette DH. 1998. Statistics of extinction and survival in Lotka–Volterra systems. Phys. Rev. E 57:44572–77
    [Google Scholar]
  2. Anderson R, May R 1992. Infectious Diseases of Humans: Dynamics and Control Oxford, UK: Oxford Univ. Press
  3. Baláž V, Williams AM. 2012. Diffusion and competition of voice communication technologies in the Czech and Slovak Republics, 1948–2009. Technol. Forecast. Soc. Change 79:2393–404
    [Google Scholar]
  4. Bass F, Jain D, Krishnan T 2000. Modelling the marketing-mix influence in new-product diffusion. New Product Diffusion Models V Mahajan, E Muller, Y Wind 99–122. New York: Springer
    [Google Scholar]
  5. Bass FM. 1969. A new product growth for model consumer durables. Manag. Sci. 15:5215–27
    [Google Scholar]
  6. Bass FM, Krishnan TV, Jain DC. 1994. Why the Bass model fits without decision variables. Mark. Sci. 13:3203–23
    [Google Scholar]
  7. Bemmaor AC 1992. Modeling the diffusion of new durable goods: word-of-mouth effect versus consumer heterogeneity. Research Traditions in Marketing G Laurent, G Lilien, B Pras 201–29. New York: Springer
    [Google Scholar]
  8. Bemmaor AC, Lee J. 2002. The impact of heterogeneity and ill-conditioning on diffusion model parameter estimates. Mark. Sci. 21:2209–20
    [Google Scholar]
  9. Bessi A, Guidolin M, Manfredi P. 2021. The role of gas on future perspectives of renewable energy diffusion: Bridging technology or lock-in?. Renew. Sustain. Energy Rev. 152:111673
    [Google Scholar]
  10. Bunea AM, Della Posta P, Guidolin M, Manfredi P 2020. What do adoption patterns of solar panels observed so far tell about governments' incentive? Insights from diffusion models. Technol. Forecast. Soc. Change 160:120240
    [Google Scholar]
  11. Centrone F, Goia A, Salinelli E. 2007. Demographic processes in a model of innovation diffusion with dynamic market. Technol. Forecast. Soc. Change 74:3247–66
    [Google Scholar]
  12. Chakrabarti AS. 2016. Stochastic Lotka–Volterra equations: a model of lagged diffusion of technology in an interconnected world. Physica A 442:214–23
    [Google Scholar]
  13. Chandrasekaran D, Tellis GJ. 2007. A critical review of marketing research on diffusion of new products. Rev. Mark. Res. 3:39–80
    [Google Scholar]
  14. Fibich G. 2016. Bass-SIR model for diffusion of new products in social networks. Phys. Rev. E 94:3032305
    [Google Scholar]
  15. Furlan C, Mortarino C. 2018. Forecasting the impact of renewable energies in competition with non-renewable sources. Renew. Sustain. Energy Rev. 81:1879–86
    [Google Scholar]
  16. Geels FW, Sovacool BK, Schwanen T, Sorrell S. 2017. Sociotechnical transitions for deep decarbonization. Science 357:63571242–44
    [Google Scholar]
  17. Goldenberg J, Libai B, Muller E. 2010. The chilling effects of network externalities. Int. J. Res. Mark. 27:14–15
    [Google Scholar]
  18. Golder PN, Tellis GJ. 1997. Will it ever fly? Modeling the takeoff of really new consumer durables. Mark. Sci. 16:3256–70
    [Google Scholar]
  19. Graziano M, Gillingham K. 2015. Spatial patterns of solar photovoltaic system adoption: the influence of neighbors and the built environment. J. Econ. Geogr. 15:4815–39
    [Google Scholar]
  20. Guidolin M, Alpcan T. 2019. Transition to sustainable energy generation in Australia: interplay between coal, gas and renewables. Renew. Energy 139:359–67
    [Google Scholar]
  21. Guidolin M, Guseo R. 2015. Technological change in the US music industry: within-product, cross-product and churn effects between competing blockbusters. Technol. Forecast. Soc. Change 99:35–46
    [Google Scholar]
  22. Guidolin M, Guseo R. 2016. The German energy transition: modeling competition and substitution between nuclear power and renewable energy technologies. Renew. Sustain. Energy Rev. 60:1498–504
    [Google Scholar]
  23. Guidolin M, Guseo R. 2020. Has the iPhone cannibalized the iPad? An asymmetric competition model. Appl. Stoch. Models Bus. Ind. 36:3465–76
    [Google Scholar]
  24. Guidolin M, Guseo R, Mortarino C. 2019. Regular and promotional sales in new product life cycles: competition and forecasting. Comput. Ind. Eng. 130:250–57
    [Google Scholar]
  25. Guidolin M, Mortarino C. 2010. Cross-country diffusion of photovoltaic systems: modelling choices and forecasts for national adoption patterns. Technol. Forecast. Soc. Change 77:2279–96
    [Google Scholar]
  26. Guseo R, Dalla Valle A, Guidolin M 2007. World oil depletion models: price effects compared with strategic or technological interventions. Technol. Forecast. Soc. Change 74:4452–69
    [Google Scholar]
  27. Guseo R, Guidolin M. 2009. Modelling a dynamic market potential: a class of automata networks for diffusion of innovations. Technol. Forecast. Soc. Change 76:6806–20
    [Google Scholar]
  28. Guseo R, Mortarino C. 2012. Sequential market entries and competition modelling in multi-innovation diffusions. Eur. J. Oper. Res. 216:3658–67
    [Google Scholar]
  29. Guseo R, Mortarino C. 2014. Within-brand and cross-brand word-of-mouth for sequential multi-innovation diffusions. IMA J. Manag. Math. 25:3287–311
    [Google Scholar]
  30. Guseo R, Mortarino C. 2015. Modeling competition between two pharmaceutical drugs using innovation diffusion models. Ann. Appl. Stat. 9:42073–89
    [Google Scholar]
  31. Hannan MT, Freeman J. 1984. Structural inertia and organizational change. Am. Sociol. Rev. 49:149–64
    [Google Scholar]
  32. Hauser J, Tellis GJ, Griffin A. 2006. Research on innovation: a review and agenda for Marketing Science. Mark. Sci. 25:6687–717
    [Google Scholar]
  33. Hethcote HW 1989. Three basic epidemiological models. Applied Mathematical Ecology S Levin, T Hallam, L Gross 119–44. New York: Springer
    [Google Scholar]
  34. Horsky D. 1990. A diffusion model incorporating product benefits, price, income and information. Mark. Sci. 9:4342–65
    [Google Scholar]
  35. Jain DC, Rao RC. 1990. Effect of price on the demand for durables: modeling, estimation, and findings. J. Bus. Econ. Stat. 8:2163–70
    [Google Scholar]
  36. Jiang Z, Bass FM, Bass PI. 2006. Virtual Bass model and the left-hand data-truncation bias in diffusion of innovation studies. Int. J. Res. Mark. 23:193–106
    [Google Scholar]
  37. Jiang Z, Jain DC. 2012. A generalized Norton–Bass model for multigeneration diffusion. Manag. Sci. 58:101887–97
    [Google Scholar]
  38. Kamakura WA, Balasubramanian SK. 1988. Long-term view of the diffusion of durables. Int. J. Res. Mark. 5:11–13
    [Google Scholar]
  39. Keeling MJ, Rohani P. 2011. Modeling Infectious Diseases in Humans and Animals Princeton, NJ: Princeton Univ. Press
  40. Kreng VB, Wang HT. 2009. A technology replacement model with variable market potential—an empirical study of CRT and LCD TV. Technol. Forecast. Soc. Change 7:76942–51
    [Google Scholar]
  41. Krishnan TV, Bass FM, Kumar V. 2000. Impact of a late entrant on the diffusion of a new product/service. J. Mark. Res. 37:2269–78
    [Google Scholar]
  42. Laciana CE, Gual G, Kalmus D, Oteiza-Aguirre N, Rovere SL. 2014. Diffusion of two brands in competition: cross-brand effect. Physica A 413:104–15
    [Google Scholar]
  43. Lotka AJ. 1920. Analytical note on certain rhythmic relations in organic systems. PNAS 6:7410–15
    [Google Scholar]
  44. Mahajan V, Muller E, Bass FM. 1990. New product diffusion models in marketing: a review and directions for research. J. Mark. 54:11–26
    [Google Scholar]
  45. Mahajan V, Muller E, Bass FM. 1995. Diffusion of new products: empirical generalizations and managerial uses. Mark. Sci. 14:3 suppl.G79–88
    [Google Scholar]
  46. Mahajan V, Peterson RA. 1978. Innovation diffusion in a dynamic potential adopter population. Manag. Sci. 24:151589–97
    [Google Scholar]
  47. Manfredi P, Bonaccorsi A, Secchi A. 1998. Social heterogeneities in classical new product diffusion models. Tech. Rep., Dip. Stat. Mat. Appl. Econ., Univ. Pisa Italy:
  48. Mansfield E. 1961. Technical change and the rate of imitation. Econometrica 29:4741–66
    [Google Scholar]
  49. Marchetti C. 1977. Primary energy substitution models: on the interaction between energy and society. Technol. Forecast. Soc. Change 10:4345–56
    [Google Scholar]
  50. Marchetti C. 1980. Society as a learning system: discovery, invention, and innovation cycles revisited. Technol. Forecast. Soc. Change 18:4267–82
    [Google Scholar]
  51. McKendrick A, Pai MK. 1912. XLV. The rate of multiplication of micro-organisms: a mathematical study. Proc. R. Soc. Edinb. 31:649–55
    [Google Scholar]
  52. Meade N, Islam T. 1995. Prediction intervals for growth curve forecasts. J. Forecast. 14:5413–30
    [Google Scholar]
  53. Meade N, Islam T. 1998. Technological forecasting—model selection, model stability, and combining models. Manag. Sci. 44:81115–30
    [Google Scholar]
  54. Meade N, Islam T. 2006. Modelling and forecasting the diffusion of innovation—a 25-year review. Int. J. Forecast. 22:3519–45
    [Google Scholar]
  55. Mesak HI, Darrat AF. 2002. Optimal pricing of new subscriber services under interdependent adoption processes. J. Serv. Res. 5:2140–53
    [Google Scholar]
  56. Morris SA, Pratt D. 2003. Analysis of the Lotka–Volterra competition equations as a technological substitution model. Technol. Forecast. Soc. Change 70:2103–33
    [Google Scholar]
  57. Newman M. 2018. Networks Oxford, UK: Oxford Univ. Press
  58. Norton JA, Bass FM. 1987. A diffusion theory model of adoption and substitution for successive generations of high-technology products. Manag. Sci. 33:91069–86
    [Google Scholar]
  59. Parker PM. 1994. Aggregate diffusion forecasting models in marketing: a critical review. Int. J. Forecast. 10:2353–80
    [Google Scholar]
  60. Pastor-Satorras R, Castellano C, Van Mieghem P, Vespignani A. 2015. Epidemic processes in complex networks. Rev. Mod. Phys. 87:3925
    [Google Scholar]
  61. Peres R, Muller E, Mahajan V. 2010. Innovation diffusion and new product growth models: a critical review and research directions. Int. J. Res. Mark. 27:291–106
    [Google Scholar]
  62. Rao KU, Kishore V. 2010. A review of technology diffusion models with special reference to renewable energy technologies. Renew. Sustain. Energy Rev. 14:31070–78
    [Google Scholar]
  63. Robert CP, Casella G. 2004. Monte Carlo Statistical Methods New York: Springer. , 2nd ed..
  64. Rogers EM. 2003. Diffusion of Innovations New York: Free Press
  65. Savin S, Terwiesch C. 2005. Optimal product launch times in a duopoly: balancing life-cycle revenues with product cost. Oper. Res. 53:126–47
    [Google Scholar]
  66. Seber GA, Wild CJ. 1989. Nonlinear Regression New York: Wiley
  67. Sharif MN, Ramanathan K. 1981. Binomial innovation diffusion models with dynamic potential adopter population. Technol. Forecast. Soc. Change 20:163–87
    [Google Scholar]
  68. Srinivasan V, Mason CH. 1986. Nonlinear least squares estimation of new product diffusion models. Mark. Sci. 5:2169–78
    [Google Scholar]
  69. Tseng FM, Liu YL, Wu HH. 2014. Market penetration among competitive innovation products: the case of the smartphone operating system. J. Eng. Technol. Manag. 32:40–59
    [Google Scholar]
  70. Tuma NB, Hannan MT. 1984. Social Dynamics Models and Methods Orlando, FL: Academic
  71. Van den Bulte C, Joshi YV. 2007. New product diffusion with influentials and imitators. Mark. Sci. 26:3400–21
    [Google Scholar]
  72. Van den Bulte C, Lilien GL. 1997. Bias and systematic change in the parameter estimates of macro-level diffusion models. Mark. Sci. 16:4338–53
    [Google Scholar]
  73. Venkatesan R, Krishnan TV, Kumar V. 2004. Evolutionary estimation of macro-level diffusion models using genetic algorithms: an alternative to nonlinear least squares. Mark. Sci. 23:3451–64
    [Google Scholar]
  74. Venkatesan R, Kumar V. 2002. A genetic algorithms approach to growth phase forecasting of wireless subscribers. Int. J. Forecast. 18:4625–46
    [Google Scholar]
  75. Verhulst PF. 1838. Notice sur la loi que la population suit dans son accroissement. Corresp. Math. Phys. 10:113–26
    [Google Scholar]
  76. Vespignani A. 2012. Modelling dynamical processes in complex socio-technical systems. Nat. Phys. 8:132–39
    [Google Scholar]
  77. Volterra V. 1926. Fluctuations in the abundance of a species considered mathematically. Nature 118:2972558–60
    [Google Scholar]
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