Innovation Diffusion Model for the Marketing of a Product with Interactions and Delay in Adoption for Two Different Patches

In this paper, an innovation diffusion model with the delay in adoption is planned to study the dynamics of the adopter of the same product within two different patches. It is determined that solutions are positive and bounded for the proposed system. Asymptotic stability analysis is carried out for all possible equilibrium points. The critical value of the delays τ 1 , τ 2 are determined. It is observed that for the interior equilibrium remains stable if either (or both) the adoption delays is (are) less than the threshold values, i.e., τ 1 < τ 10 + , τ 2 > τ 20 + or τ 1 > τ 10 + , τ 2 < τ 20 + . If both τ 1 and τ 2 cross its thresholds, system perceived oscillating behavior, and Hopf bifurcation occurs. Sensitivity analysis for the basic influence number of the model has been examined. Subsequently, numerical simulations have been carried out to support our analytical findings with the different set of parameters.