Modeling Student Organizational Engagement in Higher Education Using an Adapted SIR Dynamic System

Abstract

Student involvement in organizations is essential for developing leadership, collaboration, and broader competencies in higher education. This study analyzes the dynamics of student organizational engagement using an adapted SIR (Susceptible–Infective–Recovered) mathematical model, where the three compartments respectively represent non-members (S), active members (I), and former members (R). Parameters including recruitment rate , disengagement rate , and reactivation rate  were selected and calibrated based on prior studies in educational and social diffusion modeling. Numerical simulations conducted in MATLAB indicate convergence toward a stable equilibrium with approximately 52% non-members, 35% active members, and 13% former members, depending on parameter variation. The results also show that increasing recruitment by 50% or reducing disengagement by half accelerates system stabilization and raises the equilibrium proportion of active members by up to 20%. These findings provide quantitative insight into how organizational participation evolves dynamically and offer practical implications for universities to design data-informed policies that enhance recruitment, sustain engagement, and improve student leadership development over time.