What is the Bass Diffusion Model?

The Bass diffusion model, or merely the Bass model, is a differential equation used to describe the process involved in the adoption of new products into the population.

How is the Bass Diffusion Model Used? 

This model is used to present a rationale of the interaction between current and potential adopters of a new product. It states that there are two types of adopters - the innovators and imitators. 

This model is mathematically defined as a Riccati equation with constant coefficients. In 1833, Everett Rogers published a highly influential study describing the different stages in product adoption that was titled Diffusion of Innovations.' 

Then in 1969, a paper detailing a new model of productivity growth for consumer durables was published by Frank Bass, who contributed a few mathematical ideas to it. 

This model was discovered to fit the data of a majority of product introductions even though there was a wide range of variables in terms of managerial decisions such as pricing and advertising. 

This means that the shape of the curve is always the same despite the decision variables shifting the Bass curve in time. There is only one extension of the model that is applicable under ordinary circumstances. It was developed in 1994 by Frank Bass, Trichy Krishnan, and Dipak Jain. F(t) / 1-F(t) = (p+qF(t)) x (t)

Relationship with other S-curves

The Bass diffusion model has two special cases

• In the first special case, q=0 when the model reduces to the exponential distribution.
• In the second special case, p=0 when the model reduces to the logistic distribution.

The model is useful in estimating the size and growth rate of social networks. When compared with alternative models such as the Weibull distribution, the Bass model gives a more pessimistic view of the future according to Christian Bauchkage and his co-authors. 

Adoption of the model 

As of October 2018, the paper A New Product Growth for Model Consumer Durables' which is about the Bass model, was one of the most cited in Google Scholar with 8499 citations. In marketing and management science, this model has been widely influential. It was one of the ten most frequently cited papers back in 2004 in the history of management science.