An aggregate advertising response model based on consumer population dynamics

Aggregate advertising models are functions reflecting the relationship between product sales and advertising expenditure for a market as a whole. In this paper, we proposed a new advertising response model based on consumer population dynamics. Considering that the population dynamics is one of the basic characteristics of consumers, we try to apply it in describing the effects of advertising. In detail, a two-level framework advertising response model is introduced in this paper, in which the general Lotka-Volterra model is used to describe population dynamics among consumers and another increasing function is utilised to reflect the advertisement's effect on the intrinsic sales growth rate of a product or a brand. Mathematic analysis shows that the new advertising model has more advantages than other classic models such as Vidale-Wolfe model, Nerlove-Arrow model, Lanchester model and their modifications. Also, an early-warning marketing mechanism is introduced as an application of the proposed model.