Mathematical Model for Economic Growth, Corruption and Unemployment: Analysis of the Effects of a Time Delay in the Economic Growth

In this article, we propose a nonlinear mathematical model that incorporates a discrete time delay. The model is used to analyze the dynamics of a socioeconomic system that includes economic growth, corruption, and unemployment. We introduce the time delay in the logistic economic growth term due to the effect of the previous state of the economic growth on its current state. A local stability analysis is performed to investigate the dynamics of the socioeconomic system. We established conditions for the existence of Hopf bifurcations and the appearance of economic limit cycles. We found threshold values for the discrete-time delay in which these Hopf bifurcations occur. We corroborate the theoretical findings by performing numerical simulations for a variety of scenarios. We find various interesting socioeconomic situations where different socioeconomic limit cycles occur. Finally, we present a discussion and future directions of research.