Optimal Intervention Design for Corruption Dynamics Via Compartmental Modelling

Corruption represents a pervasive socio-economic phenomenon that undermines institutional integrity, economic development, and social cohesion globally. This research presents a comprehensive mathematical framework for modeling corruption dynamics using compartmental analysis, incorporating stability theory and optimal control strategies to design effective intervention mechanisms. We develop a deterministic compartmental model that categorizes the population into susceptible, exposed, corrupt, and recovered individuals, analogous to epidemiological models. Through rigorous stability analysis using Lyapunov theory and the next-generation matrix method, we establish conditions for corruption-free equilibrium and endemic stability. The model is extended to incorporate optimal control theory, enabling the design of cost- effective intervention strategies including awareness campaigns, legal enforcement, and rehabilitation programs. Numerical simulations demonstrate the efficacy of the proposed control mechanisms in reducing corruption prevalence while minimizing intervention costs. Our findings provide theoretical foundations for evidence-based policy design and resource allocation in anti-corruption initiatives.