Innovation diffusion model with interactions and delays in adoption for two competitive products in two different patches

The aim of the present paper, how the people behave towards the offer of two products in two different patches. In this work, an innovation diffusion model with six-compartments for two different patches is proposed. There is a delay in the adoption of product-1 in patch-2 and delay of adoption of product-2 in patch-1. The entire population in both the patches is classified into three different groups (i) non-adopter (ii) adopter of product-1 (iii) adopter of product-2. Dynamical behavior of the proposed system is studied, and Basic influence numbers (BINs) of the model are calculated. Stability analysis is executed for all the possible equilibrium points with and without delays. Hopf bifurcation analysis is too carried out taking the delay of adoption to adopt the product-1 in patch-2, and product-2 in patch-1 are bifurcation parameter and obtained the threshold values. Moreover, sensitivity analysis is carried out for the system parameter used in the interior equilibrium. Finally, exhaustive numerical simulations have been carried out by utilizing MATLAB, to supports analytical results.