Mathematical Modeling, Analysis, and Optimal Control of Corruption Dynamics

Abstract

In this paper, a nonlinear deterministic model for the dynamics of corruption is proposed and analysed qualitatively using the stability theory of differential equations. The basic reproduction number with respect to the corruption-free equilibrium is obtained using next-generation matrix method. The conditions for local and global asymptotic stability of corruption-free and endemic equilibria are established. From the analysis using center manifold theory, the model exhibits forward bifurcation. Then, the model was extended by reformulating it as an optimal control problem, with the use of two time-dependent controls to assess the impact of corruption on human population, namely, campaigning about corruption through media and advertisement and exposing corrupted individuals to jail and giving punishment. By using Pontryagin’s maximum principle, necessary conditions for the optimal control of the transmission of corruption were derived. From the numerical simulation, it was found that the integrated control strategy must be taken to fight against corruption.