A mathematical analysis of the corruption dynamics model with optimal control strategy

Abstract

Corruption is a global problem that affects many countries by destroying economic, social, and political development. Therefore, we have formulated and analyzed a mathematical model to understand better control measures that reduce corruption transmission with optimal control strategies. To verify the validity of this model, we examined a model analysis showing that the solution of the model is positive and bounded. The basic reproduction number R0 was computed by using the next-generation matrix. The formulated model was studied analytically and numerically in the context of corruption dynamics. The stability analysis of the formulated model showed that the corruption-free equilibrium is locally and globally asymptotically stable for R0 < 1, but the corruption-endemic equilibrium is globally asymptotically stable for R0 > 1. Furthermore, the optimal control strategy was expressed through the Pontryagin Maximum Principle by incorporating two control variables. Finally, numerical simulations for the optimal control model were performed using the Runge-Kutta fourth order forward and backward methods. This study showed that applying both mass education and law enforcement is the most efficient strategy to reduce the spread of corruption.