Title: Consumer behaviour-based innovation diffusion modelling using stochastic differential equation incorporating change in adoption rate

Authors: Ompal Singh; Adarsh Anand; P.K. Kapur; Deepti Aggrawal

Addresses: Department of Operational Research, Faculty of Mathematical Sciences, University of Delhi, Room No. 207, 2nd Floor, Delhi-110007, India. ' Department of Operational Research, Faculty of Mathematical Sciences, University of Delhi, Room No. 207, 2nd Floor, Delhi-110007, India. ' Amity University Campus, I-3 Block, Ground Floor, Sector-125, Noida-201301 Gautam Buddha Nagar, UP, India. ' Department of Operational Research, Faculty of Mathematical Sciences, University of Delhi, Room No. 207, 2nd Floor, Delhi-110007, India

Abstract: Bass innovation and diffusion model and many of its extended forms have been reported in marketing literature and applied successfully for predicting adoption curve of products from different segments of market. All these models assume that an adopter buys the product only once in his lifetime, however, this may not be true, because a consumer might buy the product more than once for his utility (repeat purchasing). Also, there can occur a situation that the consumer leaves the system without buying the product (balking). In this paper, we propose a diffusion model based on Itô's type of stochastic differential equation with repeat purchasing and balking. It also incorporates the change-point concept, where the rate of product adoption per remaining potential adopter might change due to shift in marketing/promotional strategy, entry/exit of some of the competitors in the market. The applicability of the proposed model is illustrated using new product sales data.

Keywords: consumer behaviour; change point; innovation diffusion; diffusion modelling; stochastic differential equations; SDE; marketing; product adoption rate; new product sales.

DOI: 10.1504/IJTMKT.2012.049592

International Journal of Technology Marketing, 2012 Vol.7 No.4, pp.346 - 360

Received: 06 Jan 2012
Accepted: 28 Jun 2012
Published online: 29 Aug 2014 *

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