A Mathematical Perspective on Corruption’s Effect on Productivity and Service Efficiency with Cost-Effective Control Strategies

Corruption remains a major barrier to development in Africa, undermining public trust, weakening service delivery, and hindering economic growth. Defined as the abuse of public power for personal gain, it appears in forms such as bribery, embezzlement, nepotism, and cronyism, affecting both public and private sectors. Despite various anti-corruption efforts, the problem persists. This study presents a non-linear system of differential equations to evaluate the impact of corruption on productivity and service delivery, incorporating both constant and time-dependent control strategies. The basic reproduction number ($R_0$) is calculated using the next-generation matrix method. Model behaviour is further analysed through sensitivity analysis and stability assessments using the Routh-Hurwitz criterion and Lyapunov functions. An optimal control framework, based on Pontryagin’s maximum principle, assesses the effectiveness and cost-efficiency of preventative and punitive interventions. Numerical simulations, using the fourth-order Runge-Kutta method, indicate that strong enforcement of punitive measures is the most effective and cost-efficient strategy to combat corruption. These measures significantly improve productivity and public service delivery. The key policy recommendation is that governments and institutions should prioritize robust punitive controls as the primary approach to reducing corruption and promoting sustainable development.