Mathematical model and stability analysis of university-PhD-postdoc-industry migration and unemployment in south Africa

Volume 31, Issue 1, pp 81--94 http://dx.doi.org/10.22436/jmcs.031.01.07

Publication Date: April 14, 2023 Submission Date: November 12, 2022 Revision Date: January 03, 2023 Accteptance Date: January 20, 2023

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Authors

A. A. Adeniji - Department of Mathematics, Tshwane University of Technology, Pretoria, South Africa. M. O. Adeniyi - Department of Mathematical Science, Lagos State University of Science and Technology, Lagos, Nigeria. M. Y. Shatalov - Department of Mathematics, Tshwane University of Technology, Pretoria, South Africa.

Abstract

Unemployment poses to be a threat in many countries which has been a long age battle with the human race. Our study considers Africa (South Africa to be precise) and focuses on the academic and industry sectors, with PhD graduates and postdoctoral research fellows as key participants. The movement of PhD graduates and postdocs between academia and industry, and its impact (increase or decrease) in unemployment within the sectors was investigated. For the population of University, PhDs, Postdocs, and industry compartments, a model was developed. The primary objectives investigates the model by analyzing the stability at the University-PhD-Postdoc-Industry free equilibrium, University-PhD-Postdoc-Industry equilibrium, determine the recruitment number $R_{UE}$ and understand how to mitigate migrations within the University and Industry compartments. Our findings help to understand the cause and effects of migration, and aims to manage the migration of PhD graduates and Postdocs moving into the Industry while the university suffers research capacities.

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Keywords

• ODE
• stability analysis
• recruitment number
• mathematical model
• Lyapunov function

MSC

•  34A34
•  81T80
•  93A30
•  97M10
•  97M70

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