Abstract

Corruption is a widespread issue with significant social and economic impacts. This study develops a compartmental model to describe the dynamics of corruption transmission and analyzes optimal control strategies to mitigate it. The model consists of four compartments: susceptible individuals, actively corrupt individuals, jailed individuals, and individuals who have completed their sentences, where the voluntary personal willingness to engage in corruption is incorporated into the model formulation. The local asymptotic stability conditions of both the corruption-free and endemic fixed points are established based on the basic reproduction number. Numerical simulation results indicate that personal willingness to engage in corrupt practices significantly enlarges the corrupt subpopulation, while the basic reproduction number remains unaffected by this personal willingness factor. By applying Pontryagin’s Maximum Principle, an optimal control strategy is formulated, and simulations demonstrate its effectiveness in reducing the corrupt subpopulation. These findings provide insights that can serve as a basis for policy measures aimed at controlling corruption.