Machine Learning and Differential Equation Models for Mathematical and Statistical Perspectives on Enrolment, Dropout, Equity, and System Concentration in Nepal’s Higher Education System

Abstract

This study develops an integrated mathematical–statistical framework for modelling enrolment growth, dropout attrition, regional equity, and institutional concentration in Nepal's higher education system. Building on Verhulst logistic growth, stock-flow compartmental dynamics, replicator-based market-share equations, and ensemble machine learning, the framework couples a system of nonlinear ordinary differential equations describing province-level enrolled, dropout, and graduate stocks with a random-forest classifier trained on survey-informed correlates of student attrition. The differential model is calibrated against documented national enrolment figures spanning 1975–2026 (University Grants Commission and Ministry of Education records) and is used to simulate seven provincial trajectories, the sensitivity of long-run attrition to a dropout-hazard parameter, the Herfindahl–Hirschman Index of institutional concentration under business-as-usual and equity-funding policy scenarios, and the interprovincial Gini coefficient of enrolment shares. The machine-learning module quantifies the relative contribution of household income, distance to campus, first-generation status, working status, gender, province-level disadvantage, and migration intent to individual dropout risk. Results show that Tribhuvan University's enrolment share, historically near 79 percent, could fall toward the high-60s percentage range within twenty-five years even under passive dynamics, and substantially faster under a funding-equalization policy; that dropout hazard is the single largest driver of long-run attrition share; and that income quantile and distance-to-campus dominate individual-level dropout risk (AUC ≈ 0.73). The framework offers policymakers a reproducible, code-based (Python/MATLAB-compatible) tool for forecasting retention, regional disparity, and institutional concentration under alternative governance and financing scenarios.