Optimal Nurse-to-Patient Staffing Models for Intensive Care Units in Nigerian Teaching Hospitals: An Analytical Approach

Intensive care unit (ICU) staffing adequacy is a critical determinant of patient mortality and healthcare worker burnout in Nigerian teaching hospitals, where chronic nurse shortages create staffing pressures that current rostering systems are ill-equipped to manage analytically. This study develops optimal nurse-to-patient staffing models for ICUs in three teaching hospitals located in Lagos, Enugu, and Kano, applying queuing theory, stochastic simulation, and integer programming within a unified analytical framework. Patient admission and discharge data covering 24 months are used to characterize ICU demand dynamics, including inter-arrival time distributions, length-of-stay distributions by diagnosis category, and acuity-adjusted nursing workload requirements per patient. Queuing models are fitted to estimate optimal bed utilization targets, and simulation models generate dynamic census forecasts under variable demand scenarios. Integer programming models then determine shift-level nurse staffing requirements that minimize cost subject to patient safety constraints derived from Ministry of Health guidelines. Results indicate that current staffing levels fall below analytically derived minimum safety thresholds on 34 percent of observed shifts across the three hospitals. The cost of achieving compliant staffing through targeted shift additions is estimated to require a 19 percent increase in nursing payroll, significantly lower than the 47 percent increase implied by blanket headcount expansion proposals. Recommendations include shift-level staffing optimization and cross-trained flexible nursing pools. Keywords: nurse staffing, ICU, integer programming, teaching hospitals, patient safety