Journal of Biological Physics

, Volume 39, Issue 1, pp 99–121 | Cite as

Analysis of recruitment and industrial human resources management for optimal productivity in the presence of the HIV/AIDS epidemic

  • Kazeem O. Okosun
  • Oluwole D. Makinde
  • Isaac Takaidza
Original Paper


The aim of this paper is to analyze the recruitment effects of susceptible and infected individuals in order to assess the productivity of an organizational labor force in the presence of HIV/AIDS with preventive and HAART treatment measures in enhancing the workforce output. We consider constant controls as well as time-dependent controls. In the constant control case, we calculate the basic reproduction number and investigate the existence and stability of equilibria. The model is found to exhibit backward and Hopf bifurcations, implying that for the disease to be eradicated, the basic reproductive number must be below a critical value of less than one. We also investigate, by calculating sensitivity indices, the sensitivity of the basic reproductive number to the model’s parameters. In the time-dependent control case, we use Pontryagin’s maximum principle to derive necessary conditions for the optimal control of the disease. Finally, numerical simulations are performed to illustrate the analytical results. The cost-effectiveness analysis results show that optimal efforts on recruitment (HIV screening of applicants, etc.) is not the most cost-effective strategy to enhance productivity in the organizational labor force. Hence, to enhance employees’ productivity, effective education programs and strict adherence to preventive measures should be promoted.


Human immunodeficiency virus (HIV) Productivity Optimal control 

Mathematics Subject Classifications (2010)

92B05 93A30 93C15 


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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Kazeem O. Okosun
    • 1
  • Oluwole D. Makinde
    • 2
  • Isaac Takaidza
    • 2
  1. 1.Department of MathematicsVaal University of TechnologyVanderbijlparkSouth Africa
  2. 2.Institute for Advance Research in Mathematical Modeling and ComputationCape Peninsula University of TechnologyCape TownSouth Africa

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