Cost-Benefit and Dynamical Investigation of a Fractional-Order Corruption Population Dynamical System

Abstract

The main objective of this study was to investigate the effects of control measures on the diffusion of corruption in the population using a fractional order approach with optimal control theory and cost-benefit analysis. The associated fractional order optimal control problem using three time-dependent control measures was reformulated. Qualitative analysis of the model investigated the model solutions that exist uniquely, the equilibrium points and their stabilities, and the corruption threshold number. Furthermore, we utilized Pontryagin’s Maximum Principle to determine the optimal solution’s existence for the fractional order optimal control problem. Through completing numerical simulations, the study also verified the theoretical results and showed that the implementation of all the proposed control measures greatly reduced corruption diffusion in the community. Eventually, the cost-effectiveness investigation proved that strategy 1, which entailed implementing protection control measures, was the most cost-effective control strategy suggested to the stakeholders for reducing and managing the corruption diffusion problem in the population.