Dynamical response by the instant buyer and thinker buyer in an innovation diffusion marketing model with media coverage

Abstract

In this exposition, a three compartment model has established to analyze the purchasing behavior of buyer. Population for a specific product marketing is classified into non-adopter group N(t), thinker group I(t) and adopter group A(t). The relation within adopter and the non-adopter group is word of mouth. For enhance the impact of word of mouth, media is the another dominating factor for impressing the non-adopter population, who has to become an adopter. In this model, there are two types of buyers instant buyers and thinker buyers. Instant purchasing is an unplanned decision to purchase a brand-new product, done just before purchase. These types of non-adopters become instant adopters. Thinker buyer is not immediate-adopter, and it will take the time for the buying of a brand-new product. Boundedness, Positivity and Basic influence numbers(BINs) of the model is studied. Stability analysis is carried out for all the possible equilibrium points. Hopf bifurcation analysis has also been determined at the adopter-free state and interior equilibrium. Sensitivity analysis for the basic reproduction number and variables about the parameters of the model has been examined for the internal steady state. Finally, numerically experimentations have been carried out to support our analytical findings with a different set of parameters.

https://doi.org/10.28919/jmcs/3496