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.
Highlights
IntroductionCorruption is an illegal activity carried out for private gain and benefit, by misuse of authority or power by public (government) or private (company) officeholders [1]
Corruption is an illegal activity carried out for private gain and benefit, by misuse of authority or power by public or private officeholders [1]
The total population NðtÞ is divided into five compartments. Those who are susceptible to corruption are susceptible individuals SðtÞ, those who are exposed to a corrupted person but do not perform it are exposed individuals EðtÞ, those who are performing corruption are corrupted individuals CðtÞ, those who stopped doing corruption are recovered individuals RðtÞ, and those who know the badness of corruption and do not perform it permanently are honest individuals HðtÞ at time t ≥ 0
Summary
Corruption is an illegal activity carried out for private gain and benefit, by misuse of authority or power by public (government) or private (company) officeholders [1]. Corruption faces a major threat to the rule of law, democracy and human rights, fairness, and social justice, hinders economic development, and brings market economies at risk for their proper and fair functioning [2, 6]. In [2], the authors developed and analysed a mathematical model for corruption dynamics. They determined the basic reproduction number and corruption-free and endemic equilibrium points. In [13], the authors developed an SIR model for the corruption dynamics They extended the model to include optimal control with a single optimal control strategy.
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