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A universal model for growth of user population of products and services

  • CHOUJUN ZHAN (a1) and CHI K. TSE (a1)


We consider a network of interacting individuals, whose actions or transitions are determined by the states (behavior) of their neighbors as well as their own personal decisions. Specifically, we develop a model according to two simple decision-making rules that can describe the growth of the user population of a newly launched product or service. We analyze 22 sets of real-world historical growth data of a variety of products and services, and show that they all follow the growth equation. The numerical procedure for finding the model parameters allows the market size, and the relative effectiveness of customer service and promotional efforts to be estimated from the available historical growth data. We study the growth profiles of products and find that for a product or service to reach a mature stage within a reasonably short time in its user growth profile, the user growth rate corresponding to influenced transitions must exceed a certain threshold. Furthermore, results show that individuals in the group of celebrities having numerous friends become users of a new product or service at a much faster rate than those connected to ordinary individuals having fewer friends.



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Albert, R., & Barabási, A.-L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74 (1), 47.
Barabási, A.-L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 289 (5439), 509512.
Buldyrev, S. V., Parshani, R., Paul, G., Stanley, H. E., & Havlin, S. (2010). Catastrophic cascade of failures in interdependent networks. Nature, 464 (7291), 10251028.
Campbell, A. (2013). Word-of-mouth communication and percolation in social networks. American Economic Review, 103 (6), 24662498.
Geroski, P. A. (2000). Models of technology diffusion. Research Policy, 29 (4), 603625.
Goldenberg, J., Libai, B., & Muller, E. (2001). Talk of the network: A complex systems look at the underlying process of word-of-mouth. Marketing Letters, 12 (3), 211223.
González-Bailón, S., Borge-Holthoefer, J., Rivero, A., & Moreno, Y. (2011). The dynamics of protest recruitment through an online network. Scientific Reports, 1, Article Number 197. DOI: 10.1038/srep00197.
Hethcote, H. W. (2000). The mathematics of infectious diseases. SIAM Review, 42 (4), 599653.
Jackson, M. O., & Rogers, B. W. (2007). Relating network structure to diffusion properties through stochastic dominance. B.E. Journal of Theoretical Economics, 7 (1), 116.
Iribarren, J. L., & Moro, E. (2011). Affinity paths and information diffusion in social networks. Social Networks, 33 (2), 134142.
Leskovec, J., & Adamic, L. A., & Huberman, B. A. (2007). The dynamics of viral marketing. ACM Transactions on the Web (TWEB), 1 (1), 146.
López-Pintado, D. (2008). Diffusion in complex social networks. Games and Economic Behavior, 62 (2), 573590.
Mendes, P., & Kell, D. (1998). Non-linear optimization of biochemical pathways: Applications to metabolic engineering and parameter estimation. Bioinformatics, 14 (10), 869883.
Moles, C. G., Mendes, P., & Banga, J. R. (2003). Parameter estimation in biochemical pathways: A comparison of global optimization methods. Genome Research, 13 (11), 24672474.
Nelson, P. (1974). Advertising as information Journal of Political Economy, 82 (4), 729754.
Pastor-Satorras, R., & Vespignani, A. (2001). Epidemic spreading in scale-free networks. Physical Review Letters, 86 (14), 3200.
Phillips, C. L., & Habor, R. D. (1995). Feedback control systems. New York: Simon & Schuster.
Shcherbakov, M. V., Brebels, A., Shcherbakova, N. L., Tyukov, A. P., Janovsky, T. A., & Kamaev, V. A. (2013). A survey of forecast error measures. World Applied Sciences Journal (Information Technologies in Modern Industry, Education & Society), 24, 171176.
Sood, A., James, G. M., & Tellis, G. J. (2009). Functional regression: A new model for predicting market penetration of new products. Marketing Science, 28 (1), 3651.
Strogatz, S. H. (2001). Exploring complex networks. Nature, 410 (8625), 268276.
Young, H. P. (2009). Innovation diffusion in heterogeneous populations: Contagion, social influence, and social learning. American Economic Review, 99 (5), 18991924.
Zhan, C., & Yeung, L. F. (2011). Parameter estimation in systems biology models using spline approximation. Bioinformatics, 5 (1), 14.


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A universal model for growth of user population of products and services

  • CHOUJUN ZHAN (a1) and CHI K. TSE (a1)


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