THE CLOSED-FORM SOLUTIONS FOR A MODEL WITH TECHNOLOGY DIFFUSION VIA LIE SYMMETRIES

A critical component of economic growth is growth in productivity which is dependent on technology adoption. While most technologies are created in developed economies, they diffuse to developing economies through various channels such as trade, migration and knowledge spillovers. In this paper, we develop the first model that integrates compartmental models with diffusion to analyze technology adoption within a framework of a system of second-order non-linear partial differential equations. We employ Lie point symmetries to derive reductions and closed-form solutions for a model of technology diffusion. A three-dimensional Lie algebra is established for the model. We utilize the combinations of Lie symmetries to obtain reductions and establish closed-form solution for the technology diffusion model. Additionally, we utilise the closed-form solution to provide graphical representations of the technology diffusion process over effective distance and over time and find the commonly observed S-curve path of technology diffusion. Furthermore, we conduct a sensitivity analysis to develop policy insights into the factors influencing the diffusion of technology.