The impact of media on a new product innovation diffusion: a mathematical model

Abstract

In this paper, we proposed a three compartment model consisting of non-adopter, adopter and frustrated classes of population to discuss the influence of media coverage in spreading and controlling of adopter of a particular product in a region. The model exhibits two equilibria:(i) a adopter-free and (ii) unique interior equilibrium. Stability analysis of the model shows that the adopter-free equilibrium is always locally asymptotically stable if the influence number of adopter $(R_0)$, which depends on parameters of the system is less than unity. Otherwise if $R_0>1$, a unique interior equilibrium exists, it is locally asymptotically stable under some set of conditions. Further analytically and numerically it is observed that the region for backward bifurcation of adopter population increases with the decrease of the valid contact rate before media alert. Finally, numerically experimentations are presented to establish the effect of different media alert rate on adopter and non adopter population.