Mathematical modeling of corruption dynamics: Exploring the role of rehabilitation of corrupt individuals

Abstract

Corruption remains a major societal challenge, and understanding its dynamics is crucial for designing effective interventions. This study develops a deterministic compartmental model to describe corruption progression among susceptible, honest, medium corrupted, active corrupted, rehabilitated, and recovered individuals. The corruption reproduction rate R c is derived, and conditions for the existence and stability of corruption-free and endemic equilibria are established. Analytical results show that R c < 1 guarantees the eventual elimination of corruption, while R c > 1 leads to persistent endemic corruption. Global sensitivity analysis using Partial Rank Correlation Coefficients combined with Latin Hypercube Sampling identifies the rehabilitation rate of active corrupted individuals ( σ ) , recovery from medium corruption ( ρ ) , and the rehabilitation coefficient ( ɛ ) as the most influential parameters in reducing corruption prevalence. Numerical simulations further demonstrate that enhanced rehabilitation accelerates recovery, suppresses medium and active corruption, and expands the recovered population. These findings highlight the critical role of rehabilitation based interventions in mitigating corruption and promoting integrity driven institutional behaviour. • The model examines how rehabilitation contributes to corruption control. • Quantifies the impact of rehabilitation on corruption prevalence. • It models corruption influence among public servants. • Simulations show prevention and reform strategies lower corruption. • Offers policy guidance for sustainable institutional integrity.