Mathematical modelling and analysis of corruption dynamics with optimal control techniques and applications

Corruption is a complex issue that affects both developed and developing countries alike. The consequences of corruption can be devastating, leading to increased poverty, inequality, and a lack of trust in public institutions. The present study introduces a nonlinear differential model that represents corruption dynamics. First, the positivity and boundedness of the model solutions are proven, and the fundamental reproduction number \(R_{0}\) is computed. Sensitivity analysis is also performed to identify the parameters that significantly influence the growth of corruption. Both the corruption-free equilibrium (CFE) and corruption-endemic equilibrium (CEE) points are calculated, and their stability is determined. The study proves that the CFE is both locally asymptotically stable (LAS) and globally asymptotically stable (GAS) if \(R_{0} < 1\) . When \(R_{0} > 1\) , the CEE point is locally and globally asymptotically stable. Finally, the proposed model is extended to an optimal control framework by introducing three time-dependent control variables, awareness, enforcement laws and rehabilitation measures to explore different strategies for reducing corruption in society. Numerical simulations by nonstandard finite difference (NSFD) method are provided to verify the theoretical results.