Revolutionizing corruption dynamics: Integrating jury influence and fractional approaches with neural network and optimal control

Corruption, a global problem, has a harmful effect that includes the deprivation of citizen rights, degradation of community faith in government institutions, disturbance of peace and security, misallocation of resources, and termination of employment chances. Although there have been numerous and varied attempts to address corruption, its enduring presence continues to pose a significant challenge in multiple countries. This research paper studies a compartmental mathematical model, that aims to clarify the dynamics of corruption transmission. The classification of population segments into five compartments is based on their intrinsic features, which enables monitoring the spread of corruption inside and across these segments. The reproduction number is calculated using advanced methodology to measure the potential for transmission. The stability of the model is examined, exhibiting both local and global asymptotic stability at the equilibrium point without corruption, as well as at the equilibrium point during the endemic state, based on the primary reproduction number. This approach is enhanced by utilizing neural networks to model and verify the intricate relationships associated with corruption dynamics. Moreover, the outcomes are verified by neural networks and tested with those obtained for the Atangana-Baleanu fractional model. Additionally, graphical illustrations are provided to depict the influence of the embedded parameters. Furthermore, the model is extended to investigate optimal control ways. Numerical simulations verify theoretical studies carried out with and without optimal control.