Mathematical Modeling of Economic Growth, Corruption, Employment and Inflation

In this paper, we construct and propose a new mathematical model to study the dynamics of economic growth, corruption, unemployment, and inflation. The proposed model includes several relationships between these social and economic factors that have been studied and presented by economists. The mathematical model has several equilibrium points that are related to different socioeconomic scenarios. We perform a stability analysis of each of these equilibrium points in order to investigate the dynamics of the socioeconomic system. We find conditions for the local stability of the equilibrium points. We present numerical simulations to illustrate the theoretical results related to the stability of the equilibrium points. Moreover, we present numerical simulations in which periodic solutions arise due to Hopf bifurcations. The model allows us to better understand the impact that inflation, corruption, and unemployment have on the dynamics of economic growth. Finally, potential avenues for future research are presented.