A mathematical view towards improving undergraduate student performance and mitigating dropout risks
Hong Zhang
Changzhou Institute of Technology
Wilson Osafo Apeanti
University of Education, Winneba
Saviour Worlanyo Akuamoah
Ho Technical University
David Yaro
Jiangsu University
Paul Georgescu
Technical University of Iaşi
Published 2021-09-01


locus of control
social influence
threshold parameters

How to Cite

Zhang H., Apeanti W. O., Akuamoah S. W., Yaro D. and Georgescu P. (2021) “A mathematical view towards improving undergraduate student performance and mitigating dropout risks”, Nonlinear Analysis: Modelling and Control, 26(5), pp. 842-860. doi: 10.15388/namc.2021.26.24120.


In this paper, we assess the relevance of social and cognitive factors such as self-efficacy, locus of control and exposure to negative social influence in relation to undergraduate student dropout. To this purpose, we analyze a compartmental model involving a system of nonlinear ODEs, which is loosely based upon the SIR model of mathematical epidemiology and describes the academic performance of the student population. We examine threshold values that govern the stability of the equilibria and can be viewed as target values to be reached in order to alleviate undergraduate students dropout. A backward bifurcation is observed to occur, analytically and numerically, provided that certain conditions are satisfied.

A sensitivity analysis is then performed to find how the threshold values respond to changes in the parameters, a procedure for estimating these parameters being also proposed. Concrete values are then computed using survey data from a Ghanaian university. The impact of parameter variation upon the dynamics of the system, particularly on certain population sizes and on threshold values, is also numerically illustrated. Our findings are then interpreted from a social cognitive perspective, realistic policy changes being proposed along with appropriate teaching and coaching strategies.

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