Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System

Zachary Kemei; Jacob Bitok; Titus Rotich

doi:doi:10.11648/j.ajam.20241206.13

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Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System

Zachary Kemei

, Jacob Bitok

, Titus Rotich^*

Published in American Journal of Applied Mathematics (Volume 12, Issue 6)

Received: 23 October 2024 Accepted: 7 November 2024 Published: 28 November 2024

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Abstract

The study of demographics is important not only for policy formulation but also for better understanding of human socio-economic characteristics, and assessment of effects of human activities on environmental impact. It is interesting to note that apart from the common population control strategies, industrialization, economic development and improvement of living standards affects population growth parameters. In this paper, an age-structured model was formulated to model population dynamics, and make predictions through simulation using 2019 Kenya population data. The age-structured mathematical model was developed, using partial differential equations on population densities as functions of age and time. The population was structured into 20 clusters each of 5 year interval, and assigned different birth, death rate and transition parameters. Crank-Nicolson numerical scheme was used to simulate the model using the 2019 parameters and population as initial conditions. It was found that; provision of social factors to an efficacy level of δ≥0.75 to a minimum of 70% population leads to a decrease of mortality rate form μ_old=0.0313 to μ_new=0.00184 and an increase in birth rate from β_old=0.02639 to β_new=0.05104. This collectively leads to an increase in population by 50% from 38,589,011 to 57,956,100 after 35 years. The initial economic dependency ratio of 1:2, was also improved due to changes in technology and improvement of living standards, to a new ratio of 1:1.14. The graphical presentation in form of a pyramid showed a trend of transition from expansive to constrictive population pyramid. This population structure is stable and remains relatively constant as long as the social factors are maintained.

Published in	American Journal of Applied Mathematics (Volume 12, Issue 6)
DOI	10.11648/j.ajam.20241206.13
Page(s)	236-245
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

Age-Structured, Constrictive, Dependency Ratio, Expansive, Population, Simulation

References

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[19]	Kemei, Z., T. Rotich, and J. Bitok, Modelling Population Dynamics Using Age-Structured System Of Partial Differential Equations.
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APA Style

Kemei, Z., Bitok, J., Rotich, T. (2024). Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System. American Journal of Applied Mathematics, 12(6), 236-245. https://doi.org/10.11648/j.ajam.20241206.13

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ACS Style

Kemei, Z.; Bitok, J.; Rotich, T. Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System. Am. J. Appl. Math. 2024, 12(6), 236-245. doi: 10.11648/j.ajam.20241206.13

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AMA Style

Kemei Z, Bitok J, Rotich T. Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System. Am J Appl Math. 2024;12(6):236-245. doi: 10.11648/j.ajam.20241206.13

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@article{10.11648/j.ajam.20241206.13,
  author = {Zachary Kemei and Jacob Bitok and Titus Rotich},
  title = {Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System
},
  journal = {American Journal of Applied Mathematics},
  volume = {12},
  number = {6},
  pages = {236-245},
  doi = {10.11648/j.ajam.20241206.13},
  url = {https://doi.org/10.11648/j.ajam.20241206.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20241206.13},
  abstract = {The study of demographics is important not only for policy formulation but also for better understanding of human socio-economic characteristics, and assessment of effects of human activities on environmental impact. It is interesting to note that apart from the common population control strategies, industrialization, economic development and improvement of living standards affects population growth parameters. In this paper, an age-structured model was formulated to model population dynamics, and make predictions through simulation using 2019 Kenya population data. The age-structured mathematical model was developed, using partial differential equations on population densities as functions of age and time. The population was structured into 20 clusters each of 5 year interval, and assigned different birth, death rate and transition parameters. Crank-Nicolson numerical scheme was used to simulate the model using the 2019 parameters and population as initial conditions. It was found that; provision of social factors to an efficacy level of δ≥0.75 to a minimum of 70% population leads to a decrease of mortality rate form μold=0.0313 to μnew=0.00184 and an increase in birth rate from βold=0.02639 to βnew=0.05104. This collectively leads to an increase in population by 50% from 38,589,011 to 57,956,100 after 35 years. The initial economic dependency ratio of 1:2, was also improved due to changes in technology and improvement of living standards, to a new ratio of 1:1.14. The graphical presentation in form of a pyramid showed a trend of transition from expansive to constrictive population pyramid. This population structure is stable and remains relatively constant as long as the social factors are maintained.
},
 year = {2024}
}

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TY  - JOUR
T1  - Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System

AU  - Zachary Kemei
AU  - Jacob Bitok
AU  - Titus Rotich
Y1  - 2024/11/28
PY  - 2024
N1  - https://doi.org/10.11648/j.ajam.20241206.13
DO  - 10.11648/j.ajam.20241206.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 236
EP  - 245
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20241206.13
AB  - The study of demographics is important not only for policy formulation but also for better understanding of human socio-economic characteristics, and assessment of effects of human activities on environmental impact. It is interesting to note that apart from the common population control strategies, industrialization, economic development and improvement of living standards affects population growth parameters. In this paper, an age-structured model was formulated to model population dynamics, and make predictions through simulation using 2019 Kenya population data. The age-structured mathematical model was developed, using partial differential equations on population densities as functions of age and time. The population was structured into 20 clusters each of 5 year interval, and assigned different birth, death rate and transition parameters. Crank-Nicolson numerical scheme was used to simulate the model using the 2019 parameters and population as initial conditions. It was found that; provision of social factors to an efficacy level of δ≥0.75 to a minimum of 70% population leads to a decrease of mortality rate form μold=0.0313 to μnew=0.00184 and an increase in birth rate from βold=0.02639 to βnew=0.05104. This collectively leads to an increase in population by 50% from 38,589,011 to 57,956,100 after 35 years. The initial economic dependency ratio of 1:2, was also improved due to changes in technology and improvement of living standards, to a new ratio of 1:1.14. The graphical presentation in form of a pyramid showed a trend of transition from expansive to constrictive population pyramid. This population structure is stable and remains relatively constant as long as the social factors are maintained.

VL  - 12
IS  - 6
ER  -

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Author Information

Zachary Kemei

Department of Mathematics and Computing, University of Eldoret, Eldoret, Kenya

Contact Email

http://orcid.org/0009-0009-5028-5247
Jacob Bitok

Department of Mathematics and Computing, University of Eldoret, Eldoret, Kenya

Contact Email

http://orcid.org/0009-0000-0139-6789
Titus Rotich

Department of Mathematics, Physics and Computing, Moi University, Eldoret, Kenya

Contact Email

http://orcid.org/0009-0003-6091-5616

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Plain Text BibTeX RIS

APA Style

Kemei, Z., Bitok, J., Rotich, T. (2024). Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System. American Journal of Applied Mathematics, 12(6), 236-245. https://doi.org/10.11648/j.ajam.20241206.13

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ACS Style

Kemei, Z.; Bitok, J.; Rotich, T. Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System. Am. J. Appl. Math. 2024, 12(6), 236-245. doi: 10.11648/j.ajam.20241206.13

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AMA Style

Kemei Z, Bitok J, Rotich T. Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System. Am J Appl Math. 2024;12(6):236-245. doi: 10.11648/j.ajam.20241206.13

Copy | Download

@article{10.11648/j.ajam.20241206.13,
  author = {Zachary Kemei and Jacob Bitok and Titus Rotich},
  title = {Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System
},
  journal = {American Journal of Applied Mathematics},
  volume = {12},
  number = {6},
  pages = {236-245},
  doi = {10.11648/j.ajam.20241206.13},
  url = {https://doi.org/10.11648/j.ajam.20241206.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajam.20241206.13},
  abstract = {The study of demographics is important not only for policy formulation but also for better understanding of human socio-economic characteristics, and assessment of effects of human activities on environmental impact. It is interesting to note that apart from the common population control strategies, industrialization, economic development and improvement of living standards affects population growth parameters. In this paper, an age-structured model was formulated to model population dynamics, and make predictions through simulation using 2019 Kenya population data. The age-structured mathematical model was developed, using partial differential equations on population densities as functions of age and time. The population was structured into 20 clusters each of 5 year interval, and assigned different birth, death rate and transition parameters. Crank-Nicolson numerical scheme was used to simulate the model using the 2019 parameters and population as initial conditions. It was found that; provision of social factors to an efficacy level of δ≥0.75 to a minimum of 70% population leads to a decrease of mortality rate form μold=0.0313 to μnew=0.00184 and an increase in birth rate from βold=0.02639 to βnew=0.05104. This collectively leads to an increase in population by 50% from 38,589,011 to 57,956,100 after 35 years. The initial economic dependency ratio of 1:2, was also improved due to changes in technology and improvement of living standards, to a new ratio of 1:1.14. The graphical presentation in form of a pyramid showed a trend of transition from expansive to constrictive population pyramid. This population structure is stable and remains relatively constant as long as the social factors are maintained.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Modeling the Effects of Social Factors on Population Dynamics Using Age-Structured System

AU  - Zachary Kemei
AU  - Jacob Bitok
AU  - Titus Rotich
Y1  - 2024/11/28
PY  - 2024
N1  - https://doi.org/10.11648/j.ajam.20241206.13
DO  - 10.11648/j.ajam.20241206.13
T2  - American Journal of Applied Mathematics
JF  - American Journal of Applied Mathematics
JO  - American Journal of Applied Mathematics
SP  - 236
EP  - 245
PB  - Science Publishing Group
SN  - 2330-006X
UR  - https://doi.org/10.11648/j.ajam.20241206.13
AB  - The study of demographics is important not only for policy formulation but also for better understanding of human socio-economic characteristics, and assessment of effects of human activities on environmental impact. It is interesting to note that apart from the common population control strategies, industrialization, economic development and improvement of living standards affects population growth parameters. In this paper, an age-structured model was formulated to model population dynamics, and make predictions through simulation using 2019 Kenya population data. The age-structured mathematical model was developed, using partial differential equations on population densities as functions of age and time. The population was structured into 20 clusters each of 5 year interval, and assigned different birth, death rate and transition parameters. Crank-Nicolson numerical scheme was used to simulate the model using the 2019 parameters and population as initial conditions. It was found that; provision of social factors to an efficacy level of δ≥0.75 to a minimum of 70% population leads to a decrease of mortality rate form μold=0.0313 to μnew=0.00184 and an increase in birth rate from βold=0.02639 to βnew=0.05104. This collectively leads to an increase in population by 50% from 38,589,011 to 57,956,100 after 35 years. The initial economic dependency ratio of 1:2, was also improved due to changes in technology and improvement of living standards, to a new ratio of 1:1.14. The graphical presentation in form of a pyramid showed a trend of transition from expansive to constrictive population pyramid. This population structure is stable and remains relatively constant as long as the social factors are maintained.

VL  - 12
IS  - 6
ER  -

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