A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors

Bridget Sena Borbor; Lewis Brew; Joseph Acquah

doi:doi:10.11648/j.ijssam.20220704.11

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A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors

Bridget Sena Borbor, Lewis Brew, Joseph Acquah

Published in International Journal of Systems Science and Applied Mathematics (Volume 7, Issue 4)

Received: 23 August 2022 Accepted: 9 September 2022 Published: 11 October 2022

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Abstract

In this paper, we developed and analyzed a non-linear ordinary differential equations model for unemployment dynamics on Ghana’s Economic Sectors. In the modelling process, seven dynamic variables were considered namely: i) number of unemployed persons in the agriculture sector, ii) number of unemployed persons in the industry sector, iii) number of unemployed persons in the service sector, iv) number of employed persons in the agriculture sector, v) number of employed persons in the industry sector, vi) number of employed persons in the service sector vii) newly created vacancies by all three sectors, We assumed that all entrants in the labour force as the total number of employed and unemployed persons of the working age group of 18 to 60 years. Entrants of the unemployment compartment are fully qualified to work at any time t, An increase in the number of unemployed is different across all three sectors. Vacancies are created collectively depending on the number of unemployed and employed persons in the agriculture, industry and service sectors. The model is studied using stability analysis by a system of differential equations. It established the behaviour of the system over time, which showed that the solution to the system is positive and bounded. The system of the equations has a non-negative equilibrium point. The Routh-Hurwitz stability criterion established the equilibrium point is locally asymptotically stable. It was observed that the stability of the model is feasible under certain conditions.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 7, Issue 4)
DOI	10.11648/j.ijssam.20220704.11
Page(s)	66-73
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Unemployment, Economic Sectors, Boundedness, Positivity, Stability, Equilibrium Point

References

[1]	Pathan, G., & Bhathawala, P. H. (2015). A Mathematical Model for Unemployment with effect of self employment. IOSR Journal of Mathematics, Vol. 11, No. 1, pp. 37-43. Available: https://doi.org/10.9790/5728-11613743
[2]	Pathan, G., & Bhathawala, P. H. (2017). A Mathematical Model for Unemployment-Taking an Action without Delay. Vol. 12, No. 1, pp. 41-48.
[3]	Anon. (2021). Ghana Statistical Service 2021 Population and Housing Census Press Release Provisional Results. In Population and Housing Census: Provisional Results. Retrieved on: November, 01, 2021. Available: https://statsghana.gov.gh/gssmain/storage/img/infobank/2021 PHC Provisional Results Press Release.pdf
[4]	Anon. (2019). Ghana Living Standards Survey round 7 (GLSS7), Main Report. In Ghana Statistical Service. Retrieved on: January 09, 2020. Available: https://statsghana.gov.gh/gsspublications.php?category=MTAwMjg3Mzk3NC4zMDc=/webstats/1opr93rn57
[5]	Anon. (2015). Integrated Business Establishment Survey: National Employment Report. Retrieved on: June 24, 2020. Available: https://www2.statsghana.gov.gh/docfiles/IBES_Questionnaires/IBES 1 reports/NATIONAL EMPLOYMENT REPORT_FINAL 24-5-16.pdf
[6]	Wray, L. R. (2009). ‘The rise and fall of money manager capitalism: A Minskian approach. Cambridge Journal of Economics, Vol. 33, No. 4, pp 807–828. Available: https://doi.org/10.1093/cje/bep024
[7]	Misra, A. K., & Singh, A. K. (2011). A mathematical model for unemployment. Nonlinear Analysis: Real World Applications, Vol. 12, No. 1, pp. 128–136. Available: https://doi.org/10.1016/j.nonrwa.2010.06.002
[8]	Misra, A. K., & Singh, A. K. (2013). A Delay Mathematical Model for the Control of Unemployment. Differential Equations and Dynamical Systems, Vol. 21, No. 3, pp. 291–307. Available: https://doi.org/10.1007/s12591-012-0153-3
[9]	Nikolopoulos, C. V., & Tzanetis, D. E. (2003). A model for housing allocation of a homeless population due to a natural disaster. Nonlinear Analysis: Real World Applications, Vol. 4, No. 4, pp. 561–579. Available: https://doi.org/10.1016/S1468-1218(02)00078-0
[10]	Weymier, E. J., & Austin, S. F. (2018). Theoretical Analysis of Nonlinear Differential Equations Theoretical Analysis of Nonlinear Differential Equations.
[11]	Strogatz, S. H. (2000). Nonlinear dynamics and chaos. In Growing Explanations. https://doi.org/10.1515/9780822390084-003
[12]	Olver, P. J. (2017). Nonlinear ordinary differential equations. In Nonlinear Ordinary Differential Equations. https://doi.org/10.1201/9780203745489
[13]	Sharov, A. A. (2021). Equilibrium: Stable or Unstable? Retrieved May 4, 2021, from https://web.ma.utexas.edu/users/davis/375/popecol/lec9/equilib.html
[14]	Edmund X DeJesus and Charles Kaufman (1987). Routh-hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations. Physical Review A, Vol. 35, No. 12, pp. 5288.

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Bridget Sena Borbor, Lewis Brew, Joseph Acquah. (2022). A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors. International Journal of Systems Science and Applied Mathematics, 7(4), 66-73. https://doi.org/10.11648/j.ijssam.20220704.11

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ACS Style

Bridget Sena Borbor; Lewis Brew; Joseph Acquah. A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors. Int. J. Syst. Sci. Appl. Math. 2022, 7(4), 66-73. doi: 10.11648/j.ijssam.20220704.11

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AMA Style

Bridget Sena Borbor, Lewis Brew, Joseph Acquah. A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors. Int J Syst Sci Appl Math. 2022;7(4):66-73. doi: 10.11648/j.ijssam.20220704.11

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@article{10.11648/j.ijssam.20220704.11,
  author = {Bridget Sena Borbor and Lewis Brew and Joseph Acquah},
  title = {A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {7},
  number = {4},
  pages = {66-73},
  doi = {10.11648/j.ijssam.20220704.11},
  url = {https://doi.org/10.11648/j.ijssam.20220704.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20220704.11},
  abstract = {In this paper, we developed and analyzed a non-linear ordinary differential equations model for unemployment dynamics on Ghana’s Economic Sectors. In the modelling process, seven dynamic variables were considered namely: i) number of unemployed persons in the agriculture sector, ii) number of unemployed persons in the industry sector, iii) number of unemployed persons in the service sector, iv) number of employed persons in the agriculture sector, v) number of employed persons in the industry sector, vi) number of employed persons in the service sector vii) newly created vacancies by all three sectors, We assumed that all entrants in the labour force as the total number of employed and unemployed persons of the working age group of 18 to 60 years. Entrants of the unemployment compartment are fully qualified to work at any time t, An increase in the number of unemployed is different across all three sectors. Vacancies are created collectively depending on the number of unemployed and employed persons in the agriculture, industry and service sectors. The model is studied using stability analysis by a system of differential equations. It established the behaviour of the system over time, which showed that the solution to the system is positive and bounded. The system of the equations has a non-negative equilibrium point. The Routh-Hurwitz stability criterion established the equilibrium point is locally asymptotically stable. It was observed that the stability of the model is feasible under certain conditions.},
 year = {2022}
}

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TY  - JOUR
T1  - A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors
AU  - Bridget Sena Borbor
AU  - Lewis Brew
AU  - Joseph Acquah
Y1  - 2022/10/11
PY  - 2022
N1  - https://doi.org/10.11648/j.ijssam.20220704.11
DO  - 10.11648/j.ijssam.20220704.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 66
EP  - 73
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20220704.11
AB  - In this paper, we developed and analyzed a non-linear ordinary differential equations model for unemployment dynamics on Ghana’s Economic Sectors. In the modelling process, seven dynamic variables were considered namely: i) number of unemployed persons in the agriculture sector, ii) number of unemployed persons in the industry sector, iii) number of unemployed persons in the service sector, iv) number of employed persons in the agriculture sector, v) number of employed persons in the industry sector, vi) number of employed persons in the service sector vii) newly created vacancies by all three sectors, We assumed that all entrants in the labour force as the total number of employed and unemployed persons of the working age group of 18 to 60 years. Entrants of the unemployment compartment are fully qualified to work at any time t, An increase in the number of unemployed is different across all three sectors. Vacancies are created collectively depending on the number of unemployed and employed persons in the agriculture, industry and service sectors. The model is studied using stability analysis by a system of differential equations. It established the behaviour of the system over time, which showed that the solution to the system is positive and bounded. The system of the equations has a non-negative equilibrium point. The Routh-Hurwitz stability criterion established the equilibrium point is locally asymptotically stable. It was observed that the stability of the model is feasible under certain conditions.
VL  - 7
IS  - 4
ER  -

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Author Information

Bridget Sena Borbor

Department of Mathematical Sciences, University of Mines and Technology (UMaT), Tarkwa, Ghana
Lewis Brew

Department of Mathematical Sciences, University of Mines and Technology (UMaT), Tarkwa, Ghana
Joseph Acquah

Department of Mathematical Sciences, University of Mines and Technology (UMaT), Tarkwa, Ghana

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APA Style

Bridget Sena Borbor, Lewis Brew, Joseph Acquah. (2022). A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors. International Journal of Systems Science and Applied Mathematics, 7(4), 66-73. https://doi.org/10.11648/j.ijssam.20220704.11

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ACS Style

Bridget Sena Borbor; Lewis Brew; Joseph Acquah. A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors. Int. J. Syst. Sci. Appl. Math. 2022, 7(4), 66-73. doi: 10.11648/j.ijssam.20220704.11

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AMA Style

Bridget Sena Borbor, Lewis Brew, Joseph Acquah. A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors. Int J Syst Sci Appl Math. 2022;7(4):66-73. doi: 10.11648/j.ijssam.20220704.11

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@article{10.11648/j.ijssam.20220704.11,
  author = {Bridget Sena Borbor and Lewis Brew and Joseph Acquah},
  title = {A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {7},
  number = {4},
  pages = {66-73},
  doi = {10.11648/j.ijssam.20220704.11},
  url = {https://doi.org/10.11648/j.ijssam.20220704.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20220704.11},
  abstract = {In this paper, we developed and analyzed a non-linear ordinary differential equations model for unemployment dynamics on Ghana’s Economic Sectors. In the modelling process, seven dynamic variables were considered namely: i) number of unemployed persons in the agriculture sector, ii) number of unemployed persons in the industry sector, iii) number of unemployed persons in the service sector, iv) number of employed persons in the agriculture sector, v) number of employed persons in the industry sector, vi) number of employed persons in the service sector vii) newly created vacancies by all three sectors, We assumed that all entrants in the labour force as the total number of employed and unemployed persons of the working age group of 18 to 60 years. Entrants of the unemployment compartment are fully qualified to work at any time t, An increase in the number of unemployed is different across all three sectors. Vacancies are created collectively depending on the number of unemployed and employed persons in the agriculture, industry and service sectors. The model is studied using stability analysis by a system of differential equations. It established the behaviour of the system over time, which showed that the solution to the system is positive and bounded. The system of the equations has a non-negative equilibrium point. The Routh-Hurwitz stability criterion established the equilibrium point is locally asymptotically stable. It was observed that the stability of the model is feasible under certain conditions.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - A Modified Non-Linear Ordinary Differential Equations Model for Unemployment Dynamics on Ghana’s Economic Sectors
AU  - Bridget Sena Borbor
AU  - Lewis Brew
AU  - Joseph Acquah
Y1  - 2022/10/11
PY  - 2022
N1  - https://doi.org/10.11648/j.ijssam.20220704.11
DO  - 10.11648/j.ijssam.20220704.11
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 66
EP  - 73
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20220704.11
AB  - In this paper, we developed and analyzed a non-linear ordinary differential equations model for unemployment dynamics on Ghana’s Economic Sectors. In the modelling process, seven dynamic variables were considered namely: i) number of unemployed persons in the agriculture sector, ii) number of unemployed persons in the industry sector, iii) number of unemployed persons in the service sector, iv) number of employed persons in the agriculture sector, v) number of employed persons in the industry sector, vi) number of employed persons in the service sector vii) newly created vacancies by all three sectors, We assumed that all entrants in the labour force as the total number of employed and unemployed persons of the working age group of 18 to 60 years. Entrants of the unemployment compartment are fully qualified to work at any time t, An increase in the number of unemployed is different across all three sectors. Vacancies are created collectively depending on the number of unemployed and employed persons in the agriculture, industry and service sectors. The model is studied using stability analysis by a system of differential equations. It established the behaviour of the system over time, which showed that the solution to the system is positive and bounded. The system of the equations has a non-negative equilibrium point. The Routh-Hurwitz stability criterion established the equilibrium point is locally asymptotically stable. It was observed that the stability of the model is feasible under certain conditions.
VL  - 7
IS  - 4
ER  -

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