Mathematical Modelling of Employee Productivity Dynamics in the Nigerian Banking Sector

Employee productivity in Nigerian commercial banks is shaped by a complex interaction of individual capability, organisational incentive structures, technology adoption, and macroeconomic operating conditions. This study develops and applies a system of differential equations to model productivity dynamics among a panel of 1,200 bank employees across 10 commercial banks headquartered in Lagos, South West Nigeria, using anonymised Human Resources data obtained under institutional agreements. The model captures feedback loops between training investment, skill accumulation, performance incentives, and productivity output, calibrated from longitudinal HR records spanning 2019 to 2023. A continuous-time optimal control problem is formulated to identify the training intensity schedule that maximises cumulative productivity gain per employee over a three-year horizon subject to budget constraints. Equilibrium analysis of the dynamic model identifies stable and unstable productivity trajectories corresponding to high-performance and low-performance workforce segments. Numerical simulation demonstrates that front-loading training investment in the first year of employment generates 28 percent higher three-year cumulative productivity compared to uniform annual training allocation. Sensitivity analysis identifies employee retention rate as the dominant parameter governing long-run productivity equilibrium. The study provides a quantitative framework for strategic human capital investment decisions in the Nigerian banking sector. Keywords: productivity modelling, differential equations, banking sector, human capital, optimal control.