Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria

Anthony Anya Okeke; Ahmed Dauda Abubakar; Jerimiah Jerry Gambo; Phidelia Ramatu Waziri-Ugwu

doi:doi:10.11648/j.mma.20200503.12

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Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria

Anthony Anya Okeke, Ahmed Dauda Abubakar, Jerimiah Jerry Gambo, Phidelia Ramatu Waziri-Ugwu

Published in Mathematical Modelling and Applications (Volume 5, Issue 3)

Received: 4 May 2020 Accepted: 25 May 2020 Published: 16 June 2020

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Abstract

In this research, we propose the use of mathematical models in determining harvesting strategies for fish farming. The work considered three logistic growth models, namely constant harvesting, periodic harvesting, and proportional harvesting model. For each of the scheme, it is estimated the optimal amount of fish harvested to protect the population from extinction. The data for this work are obtained from fish owners of selected pond in Bade (Gashua). Although, fish farming has been commercialized in Bade but there is little or no literature available in studying fish harvesting strategies. The Logistic model is appropriate for population growth of fishes when overcrowding and competition for the resource are taken into consideration. The objectives of the study where to estimate the highest continuing yield from fish harvesting strategies implemented. We compare the results obtained between the three strategies and observed the best harvesting strategy for the selected fish farm is periodic (seasonal) harvesting. The periodic harvesting strategy optimizes the harvest while maintaining stable the population of fish if the harvesting is lower or equal with the bifurcation point. Our findings can assist fish farmers in Bade, Yobe State, North East Nigeria, to increase fish supply to meet its demand and positively affect the economic growth of the area.

Published in	Mathematical Modelling and Applications (Volume 5, Issue 3)
DOI	10.11648/j.mma.20200503.12
Page(s)	138-145
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), 2020. Published by Science Publishing Group

Keywords

Biomathematics, Fishery Management, Logistic Growth Models, Harvesting, Periodic

References

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[2]	M. F. Laham, I. S. Krishnarajah, and J. M. Shariff, “Fish Harvesting Management Strategies Using Logistic Growth Model,” Sains Malaysians, vol. 41 (2), pp. 171-177, 2012.
[3]	FAO, (2009). A Fishery Manager’s Guide Book, 2^nd Ed. Editors: K. L. Cochrane and S. E. M. Garcia, John Wily & Sons, United Kindon, [Online], Available: http://www.fao.org/3/i0053e/i0053e.pdf.
[4]	V. Shehu and A. B. Spaho, “BIFURCATION ANALYSIS AS A USEFUL TOOL TO FISHERY MANAGEMENT,” Journal of Natural and Technical Sciences, Vol. 20 (2), pp. 17-26, 2015.
[5]	S. B. Adams, “Direct and Indirect Effects of channel catfish (Ictalurus punctatus) on Native Crayfishes (Cambaridae) in Experimental Tanks,” The American Midland Naturalist, 158 (1), pp. 58-95, 2007 [Online]. Avialable: https://naldc.nal.usda.gov/download/13465/PDF.
[6]	D. J. Murray, “Mathematical Biology: I. An Introduction,” 3^rd Ed, Springer, New York, 2001.
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[8]	B. Dubey, P. Chandra and P. Sinha, “A Model for fishery resource with reserve area, Nonlinear Analysis: Real World Application, vol. 4, pp. 625-637, 2003. [Online]. Available: http://home.iitk.ac.in/~peeyush/pdf/nla_bd_pc_ps.pdf.
[9]	J. Ward, P. M. Mace and E. Thunberg, “The Relationship of Fish Harvesting Capacity to Excess Capacity and Overcapacity,” Marine Resource Economics, vol. 19, pp. 525-529, 2004.
[10]	B. Mondal, A. K. Bhunia and M Maiti, “Optimal two-species harvesting policy with price and Size (biomass) of the fish population dependent catch rate function,” Applied Mathematics and Computation, vol. 187, pp. 600-608, 2007.
[11]	T. Prince, “A NEW MODEL OF HARVESTING FISH POPULATION,” International Journal of Applied Mathematics, vol. 30, no. 4. Pp. 345-350, 2017. [Online]. Available: http://www.diogenes.bg/ijam/contents/2017-30-4/6/6.pdf.
[12]	M. Fan and K. Wang, “Optimal harvesting policy for single population with periodic coefficients,” International Journal of Mathematical Biosciences, vol. 152, pp. 167-177, 1998.
[13]	W. Jing and W. Ke, “Optimal control of harvesting for single population.” Applied Mathematics and Computation 156, pp. 235-247. 2004a. [Online]. Available: http://www.paper.edu.cn/scholar/showpdf/NUD2cN1IMTT0QxeQh.
[14]	W. Jing and W. Ke,“ The optimal harvesting problems of a stage-structured population.” Applied Mathematics and Computation vol. 148, pp. 235-247., 2004b. [Online]. Available: http://www.paper.edu.cn/scholar/showpdf/NUD2cN1IMTT0MxeQh.
[15]	W. Li and K. Wang, “Optimal harvesting policy for general stochastic logistic population model,” Journal of Mathematical Analysis and Applications 368, pp. 420-428, 2010.
[16]	L. V. Idels and M. Wang, “Harvesting fisheries management strategies with modified effort function,” International Journal Modelling, Identification and Control, vol. 3 no. 1, pp. 83-87, 2008.
[17]	I. D. S. C. Michel, ”Harvesting induced fluctuations: insights from a threshold management policy,” Mathematical Biosciences, vol. 205, pp. 77-82, 2007.
[18]	Cooke, K. L. and Nusse, H. (1987). Analysis of the complicated dynamics of some harvesting models. Journal of Mathematical Biology, Vol. 25, pp 521-542.
[19]	D. Ludwig, “A theory of sustainable harvesting,” SIAM Journal of Applied Mathematics, 55 (2), pp. 564-575, 1995.
[20]	A. Daci and A. Spaho, “BIFURCATION IN A DYNAMICAL SYSTEM: HARVEST MODELS.” The 1st International Conference on Research and Educatıon–Challenges Toward the Future (ICRAE2013), 24-25 May 2013, University of Shkodra “Luigj Gurakuqi”, Shkodra, Albania. [Online]. Available: http://konferenca.unishk.edu.al/icrae2013/icraecd2013/doc/411.pdf.
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[22]	A. A. Okeke, P. R. Waziri-Ugwu, A. D. Abubakar, J. J. Gambo, “Mathematical Modelling as a Sustainable Technique for Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria,” IOSR Journal of Mathematics (IOSR-JM), e-ISSN: 2278-5728, p-ISSN: 2319-765X. Vol. 16, Issue 2 Ser. I PP 11-22, 2020. Online: http://www.iosrjournals.org/iosr-jm/papers/Vol16-issue2/Series-1/C1602011122.pdf.

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APA Style

Anthony Anya Okeke, Ahmed Dauda Abubakar, Jerimiah Jerry Gambo, Phidelia Ramatu Waziri-Ugwu. (2020). Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria. Mathematical Modelling and Applications, 5(3), 138-145. https://doi.org/10.11648/j.mma.20200503.12

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ACS Style

Anthony Anya Okeke; Ahmed Dauda Abubakar; Jerimiah Jerry Gambo; Phidelia Ramatu Waziri-Ugwu. Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria. Math. Model. Appl. 2020, 5(3), 138-145. doi: 10.11648/j.mma.20200503.12

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AMA Style

Anthony Anya Okeke, Ahmed Dauda Abubakar, Jerimiah Jerry Gambo, Phidelia Ramatu Waziri-Ugwu. Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria. Math Model Appl. 2020;5(3):138-145. doi: 10.11648/j.mma.20200503.12

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@article{10.11648/j.mma.20200503.12,
  author = {Anthony Anya Okeke and Ahmed Dauda Abubakar and Jerimiah Jerry Gambo and Phidelia Ramatu Waziri-Ugwu},
  title = {Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria},
  journal = {Mathematical Modelling and Applications},
  volume = {5},
  number = {3},
  pages = {138-145},
  doi = {10.11648/j.mma.20200503.12},
  url = {https://doi.org/10.11648/j.mma.20200503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200503.12},
  abstract = {In this research, we propose the use of mathematical models in determining harvesting strategies for fish farming. The work considered three logistic growth models, namely constant harvesting, periodic harvesting, and proportional harvesting model. For each of the scheme, it is estimated the optimal amount of fish harvested to protect the population from extinction. The data for this work are obtained from fish owners of selected pond in Bade (Gashua). Although, fish farming has been commercialized in Bade but there is little or no literature available in studying fish harvesting strategies. The Logistic model is appropriate for population growth of fishes when overcrowding and competition for the resource are taken into consideration. The objectives of the study where to estimate the highest continuing yield from fish harvesting strategies implemented. We compare the results obtained between the three strategies and observed the best harvesting strategy for the selected fish farm is periodic (seasonal) harvesting. The periodic harvesting strategy optimizes the harvest while maintaining stable the population of fish if the harvesting is lower or equal with the bifurcation point. Our findings can assist fish farmers in Bade, Yobe State, North East Nigeria, to increase fish supply to meet its demand and positively affect the economic growth of the area.},
 year = {2020}
}

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TY  - JOUR
T1  - Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria
AU  - Anthony Anya Okeke
AU  - Ahmed Dauda Abubakar
AU  - Jerimiah Jerry Gambo
AU  - Phidelia Ramatu Waziri-Ugwu
Y1  - 2020/06/16
PY  - 2020
N1  - https://doi.org/10.11648/j.mma.20200503.12
DO  - 10.11648/j.mma.20200503.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 138
EP  - 145
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20200503.12
AB  - In this research, we propose the use of mathematical models in determining harvesting strategies for fish farming. The work considered three logistic growth models, namely constant harvesting, periodic harvesting, and proportional harvesting model. For each of the scheme, it is estimated the optimal amount of fish harvested to protect the population from extinction. The data for this work are obtained from fish owners of selected pond in Bade (Gashua). Although, fish farming has been commercialized in Bade but there is little or no literature available in studying fish harvesting strategies. The Logistic model is appropriate for population growth of fishes when overcrowding and competition for the resource are taken into consideration. The objectives of the study where to estimate the highest continuing yield from fish harvesting strategies implemented. We compare the results obtained between the three strategies and observed the best harvesting strategy for the selected fish farm is periodic (seasonal) harvesting. The periodic harvesting strategy optimizes the harvest while maintaining stable the population of fish if the harvesting is lower or equal with the bifurcation point. Our findings can assist fish farmers in Bade, Yobe State, North East Nigeria, to increase fish supply to meet its demand and positively affect the economic growth of the area.
VL  - 5
IS  - 3
ER  -

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Author Information

Anthony Anya Okeke

Department of Mathematics, Faculty of Science, Federal University Gashua, Gashua, Nigeria
Ahmed Dauda Abubakar

Department of Mathematics, Faculty of Science, Federal University Gashua, Gashua, Nigeria
Jerimiah Jerry Gambo

Department of Mathematics, Faculty of Science, Federal University Gashua, Gashua, Nigeria
Phidelia Ramatu Waziri-Ugwu

Department of Agricultural Economics & Extension, Faculty of Agriculture, Federal University Gashua, Gashua, Nigeria

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APA Style

Anthony Anya Okeke, Ahmed Dauda Abubakar, Jerimiah Jerry Gambo, Phidelia Ramatu Waziri-Ugwu. (2020). Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria. Mathematical Modelling and Applications, 5(3), 138-145. https://doi.org/10.11648/j.mma.20200503.12

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ACS Style

Anthony Anya Okeke; Ahmed Dauda Abubakar; Jerimiah Jerry Gambo; Phidelia Ramatu Waziri-Ugwu. Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria. Math. Model. Appl. 2020, 5(3), 138-145. doi: 10.11648/j.mma.20200503.12

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AMA Style

Anthony Anya Okeke, Ahmed Dauda Abubakar, Jerimiah Jerry Gambo, Phidelia Ramatu Waziri-Ugwu. Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria. Math Model Appl. 2020;5(3):138-145. doi: 10.11648/j.mma.20200503.12

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@article{10.11648/j.mma.20200503.12,
  author = {Anthony Anya Okeke and Ahmed Dauda Abubakar and Jerimiah Jerry Gambo and Phidelia Ramatu Waziri-Ugwu},
  title = {Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria},
  journal = {Mathematical Modelling and Applications},
  volume = {5},
  number = {3},
  pages = {138-145},
  doi = {10.11648/j.mma.20200503.12},
  url = {https://doi.org/10.11648/j.mma.20200503.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20200503.12},
  abstract = {In this research, we propose the use of mathematical models in determining harvesting strategies for fish farming. The work considered three logistic growth models, namely constant harvesting, periodic harvesting, and proportional harvesting model. For each of the scheme, it is estimated the optimal amount of fish harvested to protect the population from extinction. The data for this work are obtained from fish owners of selected pond in Bade (Gashua). Although, fish farming has been commercialized in Bade but there is little or no literature available in studying fish harvesting strategies. The Logistic model is appropriate for population growth of fishes when overcrowding and competition for the resource are taken into consideration. The objectives of the study where to estimate the highest continuing yield from fish harvesting strategies implemented. We compare the results obtained between the three strategies and observed the best harvesting strategy for the selected fish farm is periodic (seasonal) harvesting. The periodic harvesting strategy optimizes the harvest while maintaining stable the population of fish if the harvesting is lower or equal with the bifurcation point. Our findings can assist fish farmers in Bade, Yobe State, North East Nigeria, to increase fish supply to meet its demand and positively affect the economic growth of the area.},
 year = {2020}
}

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TY  - JOUR
T1  - Mathematics as a Tool for Efficient Fishery Management and Economic Growth in Gashua, Yobe State, Nigeria
AU  - Anthony Anya Okeke
AU  - Ahmed Dauda Abubakar
AU  - Jerimiah Jerry Gambo
AU  - Phidelia Ramatu Waziri-Ugwu
Y1  - 2020/06/16
PY  - 2020
N1  - https://doi.org/10.11648/j.mma.20200503.12
DO  - 10.11648/j.mma.20200503.12
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 138
EP  - 145
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20200503.12
AB  - In this research, we propose the use of mathematical models in determining harvesting strategies for fish farming. The work considered three logistic growth models, namely constant harvesting, periodic harvesting, and proportional harvesting model. For each of the scheme, it is estimated the optimal amount of fish harvested to protect the population from extinction. The data for this work are obtained from fish owners of selected pond in Bade (Gashua). Although, fish farming has been commercialized in Bade but there is little or no literature available in studying fish harvesting strategies. The Logistic model is appropriate for population growth of fishes when overcrowding and competition for the resource are taken into consideration. The objectives of the study where to estimate the highest continuing yield from fish harvesting strategies implemented. We compare the results obtained between the three strategies and observed the best harvesting strategy for the selected fish farm is periodic (seasonal) harvesting. The periodic harvesting strategy optimizes the harvest while maintaining stable the population of fish if the harvesting is lower or equal with the bifurcation point. Our findings can assist fish farmers in Bade, Yobe State, North East Nigeria, to increase fish supply to meet its demand and positively affect the economic growth of the area.
VL  - 5
IS  - 3
ER  -

Copy | Download