Mathematical Modeling of Student Enrollment Trends in Higher Education in Nepal

Abstract

Rapid enrollment growth in Nepal’s higher education sector has outpaced the expansion of institutional capacity, faculty strength, and public investment. This study analyzed historical enrollment trends and compared mathematical models to generate projections for sectoral planning. Secondary data from the University Grants Commission Nepal, the Ministry of Education, Science and Technology, and the Central Bureau of Statistics covered the academic years 2016/17–2025/26. Linear regression, exponential growth, and logistic (Verhulst) growth models were fitted using least-squares estimation and evaluated using the coefficient of determination (R²). Enrollment increased from approximately 371,000 to 749,392 students, corresponding to a compound annual growth rate of approximately 8.1%. All three models closely fitted the historical observations, with R² values of 0.987, 0.984, and 0.987 for the linear, exponential, and logistic models, respectively. The logistic model incorporated finite enrollment capacity, estimating a long-run carrying capacity of approximately 1.57 million students. Under current conditions, it projected approximately 912,000 students by 2030, compared with 888,000 under the linear model and more than one million under the exponential model. Structural analysis identified an increase in management education’s enrollment share from 39% in 2015 to 47.1% in 2025 and a gender parity index of 1.3 in 2023/24. Community and private campuses enrolled 62% of students but were not required to report full-time faculty data, constraining assessment of staffing capacity. The findings indicate continued enrollment growth alongside capacity and reporting challenges. The study provides a quantitative basis for capacity-sensitive planning and emphasizes proportionate investment in faculty recruitment, infrastructure, and quality assurance to support sustainable expansion.