Mathematical Modeling of Mentor–Mentee Relationship via Non-linear Ordinary Differential Equations
Rajat Kaushik
Regional Institute of Education, National Council of Educational Research and Training, Bhopal-462002, Madhya Pradesh, India.
Aji Thomas
Regional Institute of Education, National Council of Educational Research and Training, Bhopal-462002, Madhya Pradesh, India.
A. K. Garg
Regional Institute of Education, National Council of Educational Research and Training, Bhopal-462002, Madhya Pradesh, India.
Ram Keval *
Department of Applied Mathematics, M. J. P. Rohilkhand University, Bareilly-243006, Uttar Pradesh, India.
*Author to whom correspondence should be addressed.
Abstract
In the teaching profession, mentoring plays a vital role in promoting effective learning and professional development. The mentor–mentee relationship acts as an important mechanism for knowledge sharing, skill enhancement, and collaborative problem-solving. In this study, we propose a two-dimensional ordinary differential equation (ODE) model to investigate the dynamics of mentor–mentee interactions. The proposed model is rigorously analyzed for positivity, boundedness, uniform permanence, and sensitivity with respect to key parameters. Furthermore, the local and global stability of the positive equilibrium point is examined using mathematical techniques. Numerical simulations are performed to support the analytical findings and to illustrate the significant impact of mentor–mentee relationships on the overall system dynamics.
Keywords: Mentor-mentee, local stability, steady states, time-plots, sensitivity analysis