Exploring Corruption Through Mathematical Modeling and Optimal Control Analysis: Examining Interactions Between Students and Employees

Corruption, defined as the misuse of authority or resources for personal gain, diverts critical resources away from essential sectors, undermining development, governance, state authority, and social cohesion. It also perpetuates other illicit activities, compounding its societal impact. Despite the ability of mathematical modeling to effectively represent complex processes, its potential in addressing corruption remains largely untapped. This study introduces a deterministic nonlinear model to analyze the dynamics of corruption using optimal control methods. Drawing on compartmental modeling, widely employed in studying the spread of phenomena analogous to infectious diseases, we adapt this framework to explore corruption within education systems. The model’s equilibria are determined, and their stability is rigorously analyzed. By leveraging Lipschitz conditions, we prove the existence and uniqueness of solutions, ensuring mathematical robustness. Our results indicate that a corruption-free equilibrium is stable when the basic reproduction number, R0, is less than one. Conversely, when R0>1, an endemic equilibrium emerges, signifying the persistence of corruption within the system. To mitigate this, we optimize control strategies based on the Pontryagin’s maximum principle. Analytical findings are further validated through comprehensive numerical simulations, providing actionable insights into the control and reduction of corruption.