A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach

Ayinde Samuel Olukayode

doi:doi:10.11648/j.ajmcm.20190401.13

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A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach

Ayinde Samuel Olukayode

Published in American Journal of Mathematical and Computer Modelling (Volume 4, Issue 1)

Received: 8 April 2019 Accepted: 23 May 2019 Published: 5 June 2019

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Abstract

Population growth rate is a factor in determining how great a burden would be imposed on a country by the changing needs of its people for infrastructure. This average annual percentage change in population is as a result of either a surplus or deficit of births rate over deaths rate and the balance of migrants entering or emigrants leaving the country. This rate may either be positive or negative. This rate is the basis used by countries for national planning and projections. Management and Control of population growth has become a singular most important national concern due to dwindling Economic fortunes and competition for essential resources. Gompertz function has always been of interest and being used by Actuaries and Demographers when analyzing population growth. In this research, an interpolating function was proposed following Gompertz function approach and a Numerical scheme was developed to solve a population growth problem. The new scheme has been tested and found to be numerically stable and convergent. The scheme is also found to be effective as the numerical solution is nearly the same as that of the analytic solution of the problem. The method is also used to predict the future population growth in Nigeria.

Published in	American Journal of Mathematical and Computer Modelling (Volume 4, Issue 1)
DOI	10.11648/j.ajmcm.20190401.13
Page(s)	21-26
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), 2019. Published by Science Publishing Group

Keywords

Gompertz Function, Mathematical Method, Population Growth, Carrying Capacity, Basis Function, Mortality Rate, Global Fertility

References

[1]	Yusufu, T. M. (2000) The Human Factor in National Development: Nigeria. First Editon. Nigeria: University of Benin Press and Spectrum Books Limited Ibadan.
[2]	Central Bank of Nigeria (2008) Statistical Bulletin: Golden Jubilee Edition.
[3]	UNDP (2000) Human Development Report, Nigeria.
[4]	Afzal, M. (2009). Population Growth and Economic Development in Pakistan. The Open Demography Journal, 2, 1-7.
[5]	Arthur L. W. (1954). Economic Development with Unlimited Supplies of Labour. Wiley Online Library. The Manchester School. Vol. 22, Issue 2.
[6]	Elaboration of data by United Nations, Department of Economic and Social Affairs, Population Division.
[7]	Eli H. T. et al. (2015). Impart of Population Growth on Economic Growth in Nigeria, 1980 – 2010, IOSR Journal of Humanities and Social Science. Vol. 20, Issue 4, pp 115–123.
[8]	Jhingan, M. L. (2005) The Economics of Development Planning. 38th Edition. New Delhi: Vrinda Publications.
[9]	Kuznets S. S. (1963). Quantitative Aspects of the Economic growth of Nations VIII: The Distribution of Income by size. Economic Development and Cultural Change, Vol. II, pp 1 & 92. Differential Equations. American Journal of Applied Mathematics and Statistics, USA. Vol. 3, No. 4, 156-160.
[10]	Nurkse, R (1961). Problems of Capital Formation in Underdeveloped Countries. New York: Oxford University Press. Pp 163.
[11]	Roston, W. W. (1962). The stages of Economic Growth. A Non-Communist Manifesto. Cambridge University Press. London. Pp 2,38,59.
[12]	United Nations Systems in Nigeria (2001) Nigeria: Common Country Assessment.
[13]	Todaro, M. and Smith, S. (2006) Economic Development. Ninth Edition. U. S. A. Pearson Publishing Company.
[14]	Ayinde S. O., Ibijola E. A., (2015). A New Numerical Method for Solving First Order
[15]	Ogunrinde R. B., Ayinde S. O. (2018). Interpolating and Gompertz Function Approach in Tumour Growth Analysis. Americal Journal of Mathematics and Statistics. 8(5), 119–125.
[16]	Samuel Olukayode Ayinde, Roseline Bosede Ogunrinde (2018). Mathematical Integration for solving Biological Growth in Fish Lake Problem using Gompertz Approach. Biomedical Statistics and Informatics. 3(3), 43–48.
[17]	Ogunrinde R. B. and Ayinde S. O. (2017). A Numerical Integration for Solving First Order Differential Equations using Gompertz Function Approach. American Journal of Computational and Applied Mathematics. 7(6): 143 – 148.
[18]	Winsor, C. P. (1932). “The Gompertz Curve as a Growth Curve”. Proceedings of the National Academy of Sciences. Vol 18, No 1, 1-8.
[19]	Henrici, P. (1962), Discrete Variable Methods in ODEs, New York: John Wiley & Sons.
[20]	UNFPA (1999) The State of World Population 1999. UNFPA, New York.
[21]	UN (2000) Key Actions for the Further Implementation of the Programme of Action of the International Conference on Population and Development. New York, June – July 1999.

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Ayinde Samuel Olukayode. (2019). A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach. American Journal of Mathematical and Computer Modelling, 4(1), 21-26. https://doi.org/10.11648/j.ajmcm.20190401.13

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Ayinde Samuel Olukayode. A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach. Am. J. Math. Comput. Model. 2019, 4(1), 21-26. doi: 10.11648/j.ajmcm.20190401.13

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AMA Style

Ayinde Samuel Olukayode. A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach. Am J Math Comput Model. 2019;4(1):21-26. doi: 10.11648/j.ajmcm.20190401.13

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@article{10.11648/j.ajmcm.20190401.13,
  author = {Ayinde Samuel Olukayode},
  title = {A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {4},
  number = {1},
  pages = {21-26},
  doi = {10.11648/j.ajmcm.20190401.13},
  url = {https://doi.org/10.11648/j.ajmcm.20190401.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20190401.13},
  abstract = {Population growth rate is a factor in determining how great a burden would be imposed on a country by the changing needs of its people for infrastructure. This average annual percentage change in population is as a result of either a surplus or deficit of births rate over deaths rate and the balance of migrants entering or emigrants leaving the country. This rate may either be positive or negative. This rate is the basis used by countries for national planning and projections. Management and Control of population growth has become a singular most important national concern due to dwindling Economic fortunes and competition for essential resources. Gompertz function has always been of interest and being used by Actuaries and Demographers when analyzing population growth. In this research, an interpolating function was proposed following Gompertz function approach and a Numerical scheme was developed to solve a population growth problem. The new scheme has been tested and found to be numerically stable and convergent. The scheme is also found to be effective as the numerical solution is nearly the same as that of the analytic solution of the problem. The method is also used to predict the future population growth in Nigeria.},
 year = {2019}
}

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TY  - JOUR
T1  - A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach
AU  - Ayinde Samuel Olukayode
Y1  - 2019/06/05
PY  - 2019
N1  - https://doi.org/10.11648/j.ajmcm.20190401.13
DO  - 10.11648/j.ajmcm.20190401.13
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 21
EP  - 26
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20190401.13
AB  - Population growth rate is a factor in determining how great a burden would be imposed on a country by the changing needs of its people for infrastructure. This average annual percentage change in population is as a result of either a surplus or deficit of births rate over deaths rate and the balance of migrants entering or emigrants leaving the country. This rate may either be positive or negative. This rate is the basis used by countries for national planning and projections. Management and Control of population growth has become a singular most important national concern due to dwindling Economic fortunes and competition for essential resources. Gompertz function has always been of interest and being used by Actuaries and Demographers when analyzing population growth. In this research, an interpolating function was proposed following Gompertz function approach and a Numerical scheme was developed to solve a population growth problem. The new scheme has been tested and found to be numerically stable and convergent. The scheme is also found to be effective as the numerical solution is nearly the same as that of the analytic solution of the problem. The method is also used to predict the future population growth in Nigeria.
VL  - 4
IS  - 1
ER  -

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Author Information

Ayinde Samuel Olukayode

Department of Mathematics, Faculty of Science, Ekiti State University, Ado Ekiti, Nigeria

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APA Style

Ayinde Samuel Olukayode. (2019). A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach. American Journal of Mathematical and Computer Modelling, 4(1), 21-26. https://doi.org/10.11648/j.ajmcm.20190401.13

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ACS Style

Ayinde Samuel Olukayode. A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach. Am. J. Math. Comput. Model. 2019, 4(1), 21-26. doi: 10.11648/j.ajmcm.20190401.13

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AMA Style

Ayinde Samuel Olukayode. A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach. Am J Math Comput Model. 2019;4(1):21-26. doi: 10.11648/j.ajmcm.20190401.13

Copy | Download

@article{10.11648/j.ajmcm.20190401.13,
  author = {Ayinde Samuel Olukayode},
  title = {A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {4},
  number = {1},
  pages = {21-26},
  doi = {10.11648/j.ajmcm.20190401.13},
  url = {https://doi.org/10.11648/j.ajmcm.20190401.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20190401.13},
  abstract = {Population growth rate is a factor in determining how great a burden would be imposed on a country by the changing needs of its people for infrastructure. This average annual percentage change in population is as a result of either a surplus or deficit of births rate over deaths rate and the balance of migrants entering or emigrants leaving the country. This rate may either be positive or negative. This rate is the basis used by countries for national planning and projections. Management and Control of population growth has become a singular most important national concern due to dwindling Economic fortunes and competition for essential resources. Gompertz function has always been of interest and being used by Actuaries and Demographers when analyzing population growth. In this research, an interpolating function was proposed following Gompertz function approach and a Numerical scheme was developed to solve a population growth problem. The new scheme has been tested and found to be numerically stable and convergent. The scheme is also found to be effective as the numerical solution is nearly the same as that of the analytic solution of the problem. The method is also used to predict the future population growth in Nigeria.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - A Numerical Analysis of Basis Function on Population Growth Using Gompertz Approach
AU  - Ayinde Samuel Olukayode
Y1  - 2019/06/05
PY  - 2019
N1  - https://doi.org/10.11648/j.ajmcm.20190401.13
DO  - 10.11648/j.ajmcm.20190401.13
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 21
EP  - 26
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20190401.13
AB  - Population growth rate is a factor in determining how great a burden would be imposed on a country by the changing needs of its people for infrastructure. This average annual percentage change in population is as a result of either a surplus or deficit of births rate over deaths rate and the balance of migrants entering or emigrants leaving the country. This rate may either be positive or negative. This rate is the basis used by countries for national planning and projections. Management and Control of population growth has become a singular most important national concern due to dwindling Economic fortunes and competition for essential resources. Gompertz function has always been of interest and being used by Actuaries and Demographers when analyzing population growth. In this research, an interpolating function was proposed following Gompertz function approach and a Numerical scheme was developed to solve a population growth problem. The new scheme has been tested and found to be numerically stable and convergent. The scheme is also found to be effective as the numerical solution is nearly the same as that of the analytic solution of the problem. The method is also used to predict the future population growth in Nigeria.
VL  - 4
IS  - 1
ER  -

Copy | Download