Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach

Samuel Olukayode Ayinde; Roseline Bosede Ogunrinde

doi:doi:10.11648/j.bsi.20180303.11

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Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach

Samuel Olukayode Ayinde, Roseline Bosede Ogunrinde

Published in Biomedical Statistics and Informatics (Volume 3, Issue 3)

Received: 6 July 2018 Accepted: 3 August 2018 Published: 31 August 2018

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Abstract

A lake is classified as a body of relatively still water that is almost completely surrounded by land with a river or stream that feeds into it or drains from it. A lake that has fish that you can catch can either be man-made or natural, with natural lakes tending to have more successful results. In this research, an interpolating function was proposed following Gompertz function approach considering the scale and shape parameters, a Numerical Method was developed and applied to solve the biological fish lake stocking and growth problem which gives effective results as when Gompertz equation was used directly. Numerical method is an effective tool to solve the problem of growth as its applicable in Gompertz equation. The method results obtained found to be favourable when the Numerical Solution and Analytical Solution is compared as the error obtained is minimal showing the effectiveness of the Method. Gompertz Function or equation was for long of interest only to actuaries and demographics. Its however, recently been used by various authors as a growth curve or function both for biological, economics and Management phenomena. Therefore, we have been able to show how the numerical integration obtained from the interpolating function work the same way Gompertz function worked.

Published in	Biomedical Statistics and Informatics (Volume 3, Issue 3)
DOI	10.11648/j.bsi.20180303.11
Page(s)	43-48
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), 2018. Published by Science Publishing Group

Keywords

Gompertz Equation, Mathematical Integration, Logistic Growth, Carrying Capacity

References

[1]	Winsor, C. P. (1932). “The Gompertz Curve as a Growth Curve”. Proceedings of the National Academy of Sciences. Vol 18. No 1, 1-7.
[2]	Wilderbuera, T. K. and Zhang, C. (1999). “Evaluation of the Population Dynamics and Yield”. Characterisitics of Alaska place, Pleuronects quadrituberculatus in the Easten Bering Sea. Fisheries Research. Vol. 41, issue 2.
[3]	Richard W. Z., Chris J. H., Stephen L. K., Thomas P. G., and Philip S. L. (2003). “Ecologically Sustainable Yield”. Archived 2011/06/11 at the Wayback Machine. American Scientist. March-April.
[4]	Mickens, R. E. (1994). “Non-Standard Finite Difference Models of Differential Equations”. World Scientific, Singapore.
[5]	Caswell, H. (2001). “Matrix Population Models: Construction, Analysis and Interpretation”. 2nd Edition, Sinauer Associates. Sunderland, Maassachusetts.
[6]	Ogunrinde R. B., and Ayinde S. O. (2017). “A Numerical Integration for Solving First Order Differential Equation Using Gompertz Function Approach”. American Journal of Computational and Applied Mathematics. 7(6): 143 – 148.
[7]	Caswell, H. (2006). “Population Models: Analysis and Interpretation”. 3rd Edition, Sinauer Associates. Sunderland, Maassachusetts.
[8]	Walters C. and Maguire J. (1996). “Lessons for Stock assessment from the Northern Cod Collapse”. Reviews in fish Biology and Fisheries. 6:125–137
[9]	Richards F. J. (1959). “A Flexible Growth Function for Empirical Use”. Journal of Experimental Bothany. 10:290-301.
[10]	Cheng B. (2011). “MAT274 HM 2 Solutions”. Arisona State University. School of Mathematical and Statistical Sciences. USA.
[11]	www://en.m.wikipedia.org/…/Population 2017/03/12.
[12]	Kapur V., Troy D. and Oris J. (1997). “A Sustainable Fishing Simulation Using Mathematical Modeling.” Crossroads.

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APA Style

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. https://doi.org/10.11648/j.bsi.20180303.11

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ACS Style

Samuel Olukayode Ayinde; Roseline Bosede Ogunrinde. Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach. Biomed. Stat. Inform. 2018, 3(3), 43-48. doi: 10.11648/j.bsi.20180303.11

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AMA Style

Samuel Olukayode Ayinde, Roseline Bosede Ogunrinde. Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach. Biomed Stat Inform. 2018;3(3):43-48. doi: 10.11648/j.bsi.20180303.11

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@article{10.11648/j.bsi.20180303.11,
  author = {Samuel Olukayode Ayinde and Roseline Bosede Ogunrinde},
  title = {Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach},
  journal = {Biomedical Statistics and Informatics},
  volume = {3},
  number = {3},
  pages = {43-48},
  doi = {10.11648/j.bsi.20180303.11},
  url = {https://doi.org/10.11648/j.bsi.20180303.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20180303.11},
  abstract = {A lake is classified as a body of relatively still water that is almost completely surrounded by land with a river or stream that feeds into it or drains from it. A lake that has fish that you can catch can either be man-made or natural, with natural lakes tending to have more successful results. In this research, an interpolating function was proposed following Gompertz function approach considering the scale and shape parameters, a Numerical Method was developed and applied to solve the biological fish lake stocking and growth problem which gives effective results as when Gompertz equation was used directly. Numerical method is an effective tool to solve the problem of growth as its applicable in Gompertz equation. The method results obtained found to be favourable when the Numerical Solution and Analytical Solution is compared as the error obtained is minimal showing the effectiveness of the Method. Gompertz Function or equation was for long of interest only to actuaries and demographics. Its however, recently been used by various authors as a growth curve or function both for biological, economics and Management phenomena. Therefore, we have been able to show how the numerical integration obtained from the interpolating function work the same way Gompertz function worked.},
 year = {2018}
}

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TY  - JOUR
T1  - Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach
AU  - Samuel Olukayode Ayinde
AU  - Roseline Bosede Ogunrinde
Y1  - 2018/08/31
PY  - 2018
N1  - https://doi.org/10.11648/j.bsi.20180303.11
DO  - 10.11648/j.bsi.20180303.11
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 43
EP  - 48
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20180303.11
AB  - A lake is classified as a body of relatively still water that is almost completely surrounded by land with a river or stream that feeds into it or drains from it. A lake that has fish that you can catch can either be man-made or natural, with natural lakes tending to have more successful results. In this research, an interpolating function was proposed following Gompertz function approach considering the scale and shape parameters, a Numerical Method was developed and applied to solve the biological fish lake stocking and growth problem which gives effective results as when Gompertz equation was used directly. Numerical method is an effective tool to solve the problem of growth as its applicable in Gompertz equation. The method results obtained found to be favourable when the Numerical Solution and Analytical Solution is compared as the error obtained is minimal showing the effectiveness of the Method. Gompertz Function or equation was for long of interest only to actuaries and demographics. Its however, recently been used by various authors as a growth curve or function both for biological, economics and Management phenomena. Therefore, we have been able to show how the numerical integration obtained from the interpolating function work the same way Gompertz function worked.
VL  - 3
IS  - 3
ER  -

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Author Information

Samuel Olukayode Ayinde

Department of Mathematics, Faculty of Science, Ekiti State University, Ado Ekiti, Nigeria
Roseline Bosede Ogunrinde

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

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Plain Text BibTeX RIS

APA Style

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. https://doi.org/10.11648/j.bsi.20180303.11

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ACS Style

Samuel Olukayode Ayinde; Roseline Bosede Ogunrinde. Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach. Biomed. Stat. Inform. 2018, 3(3), 43-48. doi: 10.11648/j.bsi.20180303.11

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AMA Style

Samuel Olukayode Ayinde, Roseline Bosede Ogunrinde. Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach. Biomed Stat Inform. 2018;3(3):43-48. doi: 10.11648/j.bsi.20180303.11

Copy | Download

@article{10.11648/j.bsi.20180303.11,
  author = {Samuel Olukayode Ayinde and Roseline Bosede Ogunrinde},
  title = {Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach},
  journal = {Biomedical Statistics and Informatics},
  volume = {3},
  number = {3},
  pages = {43-48},
  doi = {10.11648/j.bsi.20180303.11},
  url = {https://doi.org/10.11648/j.bsi.20180303.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.bsi.20180303.11},
  abstract = {A lake is classified as a body of relatively still water that is almost completely surrounded by land with a river or stream that feeds into it or drains from it. A lake that has fish that you can catch can either be man-made or natural, with natural lakes tending to have more successful results. In this research, an interpolating function was proposed following Gompertz function approach considering the scale and shape parameters, a Numerical Method was developed and applied to solve the biological fish lake stocking and growth problem which gives effective results as when Gompertz equation was used directly. Numerical method is an effective tool to solve the problem of growth as its applicable in Gompertz equation. The method results obtained found to be favourable when the Numerical Solution and Analytical Solution is compared as the error obtained is minimal showing the effectiveness of the Method. Gompertz Function or equation was for long of interest only to actuaries and demographics. Its however, recently been used by various authors as a growth curve or function both for biological, economics and Management phenomena. Therefore, we have been able to show how the numerical integration obtained from the interpolating function work the same way Gompertz function worked.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Mathematical Integration for Solving Biological Growth in Fish Lake Problem Using Gompertz Approach
AU  - Samuel Olukayode Ayinde
AU  - Roseline Bosede Ogunrinde
Y1  - 2018/08/31
PY  - 2018
N1  - https://doi.org/10.11648/j.bsi.20180303.11
DO  - 10.11648/j.bsi.20180303.11
T2  - Biomedical Statistics and Informatics
JF  - Biomedical Statistics and Informatics
JO  - Biomedical Statistics and Informatics
SP  - 43
EP  - 48
PB  - Science Publishing Group
SN  - 2578-8728
UR  - https://doi.org/10.11648/j.bsi.20180303.11
AB  - A lake is classified as a body of relatively still water that is almost completely surrounded by land with a river or stream that feeds into it or drains from it. A lake that has fish that you can catch can either be man-made or natural, with natural lakes tending to have more successful results. In this research, an interpolating function was proposed following Gompertz function approach considering the scale and shape parameters, a Numerical Method was developed and applied to solve the biological fish lake stocking and growth problem which gives effective results as when Gompertz equation was used directly. Numerical method is an effective tool to solve the problem of growth as its applicable in Gompertz equation. The method results obtained found to be favourable when the Numerical Solution and Analytical Solution is compared as the error obtained is minimal showing the effectiveness of the Method. Gompertz Function or equation was for long of interest only to actuaries and demographics. Its however, recently been used by various authors as a growth curve or function both for biological, economics and Management phenomena. Therefore, we have been able to show how the numerical integration obtained from the interpolating function work the same way Gompertz function worked.
VL  - 3
IS  - 3
ER  -

Copy | Download