Dynamical analysis of fractional order corruption diffusion model with optimal control and cost-effectiveness analysis

Corruption persists globally, yet most mathematical models oversimplify it. This study introduces a seven-compartment fractional-order model capturing chronic entrenchment and relapse. Memory effects reveal societal inertia: past experiences buffer rapid moral decline but make recovery slow once corruption takes hold. Prevention emerges as the most effective and cost-efficient strategy, outperforming treatment alone. Combining prevention with targeted treatment creates synergy, reliably reducing corruption below the endemic threshold. These findings provide policymakers a quantitative basis for prioritizing transparency and ethics education while focusing rehabilitation on breaking the chronic-relapse cycle.