Sensitivity Analysis of Parameters in a Competition Model

Frank Nathan Ngoteya; Yaw Nkansah-Gyekye

doi:doi:10.11648/j.acm.20150405.15

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Sensitivity Analysis of Parameters in a Competition Model

Frank Nathan Ngoteya, Yaw Nkansah-Gyekye

Published in Applied and Computational Mathematics (Volume 4, Issue 5)

Received: 27 August 2015 Accepted: 8 September 2015 Published: 22 September 2015

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Abstract

Competition models may be used by ecologists as basic guidelines in analyzing issues that contribute to the decline of species population. To be used for that purpose, a mathematical model must be prudently parameterized. Therefore, this paper examines the effects of interference competition by lions with human–related mortality to the population dynamics of African wild dogs. The model was carefully parameterized and validated with estimated data by employing the theory of basic reproduction number and by running the sensitivity analysis. Numerical simulation of the model was executed by using MATLAB to explore the outcome of certain key parameters when changes are applied on them.

Published in	Applied and Computational Mathematics (Volume 4, Issue 5)
DOI	10.11648/j.acm.20150405.15
Page(s)	363-368
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), 2015. Published by Science Publishing Group

Keywords

Interference Competition, African Wild Dog, Lion, Basic Reproduction Number, Sensitivity Analysis

References

[1]	Baigent, S., 2010. Lotka-Volterra Dynamics- An Introduction. [Online] Available at: http://www.ltcc.ac.uk/courses/BioMathematics/LTCC LV2010 [Accessed 8 4 2015].
[2]	Blanco, K., Barley, K., and Mubayi, A., 2014. Population Dynamics of Wolves and Coyotes at Yellowstone National Park: Modeling Interference Competition with an Infectious Disease. pp. 2-5.
[3]	Caut, S., Casanovas, J. G., Virgos, E., Lozano, J., Witmer, G. W., and Courchamp, F., 2007. Rats dying for mice: Modelling the competitor Release Effect. Austral Ecology, Issue 32, pp. 858 - 868.
[4]	Chitnis, N., Hyman, J. and Cusching, J. M., 2008. Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model. Bull. Math. Biol., 5(70), pp. 1272-1296.
[5]	Cronin, J. P. and Carson, W. P., 2015. Biology Encyclopedia Forum. [Online] Available at: http://www.biologyreference.com/Ce-Co/Competition.html [Accessed 18 August 2015].
[6]	Dutson, G. and Sillero-Zubiri, C., 2005. Forest-dwelling African wild dogs in the Bale Mountains, Ethiopia. [Online] Available at: http://www.canids.org/canisnews/8/African_wild_dogs_in_Ethiopia.pdf [Accessed 31 May 2015].
[7]	IUCN Red List, 2008. Endangered Species. [Online] Available at: http://www.iucnredlist.org/ [Accessed 27 May 2015].
[8]	Lozano, J., Casanovas, J. G., Virgos, E. and Zorrila, J., 2013. The competitor Release Effect applied to carnivore species: How Red Foxes can Increase in numbers when persecuted. Animal Biodiversity and Conservation, Issue 36.1, p. 39.
[9]	Mikucki, M. A., 2012. Sensitivity analysis of the basic reproduction number and other quantities for infectious disease models, Colorado: Colorado State University.
[10]	Nakayama, S. and Fuiman, L. A., 2010. Body size and vigilance mediate asymmetric interference competition for food in fish larvae, Oxford: Oxford University Press.
[11]	Painted Dog Conservation Incorporated, 2014. Threats. [Online] Available at: http://www.painteddogconservation.iinet.net.au [Accessed 28 May 2015].
[12]	Sillero-Zubiri, C., Hoffmann, M. and Macdonald, D. W., 2004. Canids: Foxes, Wolves, Jackals and Dogs: Status and Conservation Action Plan, Gland, Switzerland and Cambridge, UK: IUCN/SSC Canid Specialist Group.
[13]	Van den Driessche, P. and Watmough, J., 2002. Reproduction Numbers and Sub-Threshold Endemic Equilibria for Compartmental Models of Disease Transmission. Mathematical Biosciences, Issue 180, pp. 29 - 48.
[14]	Woodroffe, R., Ginsberg, J., Macdonald, D. and IUCN/SSC Canid Specialists, 1997. The African Wild Dog - Status Survey and Conservation Action Plan. Gland, Switzerland: IUCN.

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Frank Nathan Ngoteya, Yaw Nkansah-Gyekye. (2015). Sensitivity Analysis of Parameters in a Competition Model. Applied and Computational Mathematics, 4(5), 363-368. https://doi.org/10.11648/j.acm.20150405.15

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Frank Nathan Ngoteya; Yaw Nkansah-Gyekye. Sensitivity Analysis of Parameters in a Competition Model. Appl. Comput. Math. 2015, 4(5), 363-368. doi: 10.11648/j.acm.20150405.15

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Frank Nathan Ngoteya, Yaw Nkansah-Gyekye. Sensitivity Analysis of Parameters in a Competition Model. Appl Comput Math. 2015;4(5):363-368. doi: 10.11648/j.acm.20150405.15

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@article{10.11648/j.acm.20150405.15,
  author = {Frank Nathan Ngoteya and Yaw Nkansah-Gyekye},
  title = {Sensitivity Analysis of Parameters in a Competition Model},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {5},
  pages = {363-368},
  doi = {10.11648/j.acm.20150405.15},
  url = {https://doi.org/10.11648/j.acm.20150405.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150405.15},
  abstract = {Competition models may be used by ecologists as basic guidelines in analyzing issues that contribute to the decline of species population. To be used for that purpose, a mathematical model must be prudently parameterized. Therefore, this paper examines the effects of interference competition by lions with human–related mortality to the population dynamics of African wild dogs. The model was carefully parameterized and validated with estimated data by employing the theory of basic reproduction number and by running the sensitivity analysis. Numerical simulation of the model was executed by using MATLAB to explore the outcome of certain key parameters when changes are applied on them.},
 year = {2015}
}

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TY  - JOUR
T1  - Sensitivity Analysis of Parameters in a Competition Model
AU  - Frank Nathan Ngoteya
AU  - Yaw Nkansah-Gyekye
Y1  - 2015/09/22
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150405.15
DO  - 10.11648/j.acm.20150405.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 363
EP  - 368
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150405.15
AB  - Competition models may be used by ecologists as basic guidelines in analyzing issues that contribute to the decline of species population. To be used for that purpose, a mathematical model must be prudently parameterized. Therefore, this paper examines the effects of interference competition by lions with human–related mortality to the population dynamics of African wild dogs. The model was carefully parameterized and validated with estimated data by employing the theory of basic reproduction number and by running the sensitivity analysis. Numerical simulation of the model was executed by using MATLAB to explore the outcome of certain key parameters when changes are applied on them.
VL  - 4
IS  - 5
ER  -

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Author Information

Frank Nathan Ngoteya

Applied Mathematics Department, the Nelson Mandela African Institute of Science and Technology, Arusha, Tanzania
Yaw Nkansah-Gyekye

Applied Mathematics Department, the Nelson Mandela African Institute of Science and Technology, Arusha, Tanzania

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Frank Nathan Ngoteya, Yaw Nkansah-Gyekye. (2015). Sensitivity Analysis of Parameters in a Competition Model. Applied and Computational Mathematics, 4(5), 363-368. https://doi.org/10.11648/j.acm.20150405.15

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ACS Style

Frank Nathan Ngoteya; Yaw Nkansah-Gyekye. Sensitivity Analysis of Parameters in a Competition Model. Appl. Comput. Math. 2015, 4(5), 363-368. doi: 10.11648/j.acm.20150405.15

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AMA Style

Frank Nathan Ngoteya, Yaw Nkansah-Gyekye. Sensitivity Analysis of Parameters in a Competition Model. Appl Comput Math. 2015;4(5):363-368. doi: 10.11648/j.acm.20150405.15

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@article{10.11648/j.acm.20150405.15,
  author = {Frank Nathan Ngoteya and Yaw Nkansah-Gyekye},
  title = {Sensitivity Analysis of Parameters in a Competition Model},
  journal = {Applied and Computational Mathematics},
  volume = {4},
  number = {5},
  pages = {363-368},
  doi = {10.11648/j.acm.20150405.15},
  url = {https://doi.org/10.11648/j.acm.20150405.15},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20150405.15},
  abstract = {Competition models may be used by ecologists as basic guidelines in analyzing issues that contribute to the decline of species population. To be used for that purpose, a mathematical model must be prudently parameterized. Therefore, this paper examines the effects of interference competition by lions with human–related mortality to the population dynamics of African wild dogs. The model was carefully parameterized and validated with estimated data by employing the theory of basic reproduction number and by running the sensitivity analysis. Numerical simulation of the model was executed by using MATLAB to explore the outcome of certain key parameters when changes are applied on them.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Sensitivity Analysis of Parameters in a Competition Model
AU  - Frank Nathan Ngoteya
AU  - Yaw Nkansah-Gyekye
Y1  - 2015/09/22
PY  - 2015
N1  - https://doi.org/10.11648/j.acm.20150405.15
DO  - 10.11648/j.acm.20150405.15
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 363
EP  - 368
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20150405.15
AB  - Competition models may be used by ecologists as basic guidelines in analyzing issues that contribute to the decline of species population. To be used for that purpose, a mathematical model must be prudently parameterized. Therefore, this paper examines the effects of interference competition by lions with human–related mortality to the population dynamics of African wild dogs. The model was carefully parameterized and validated with estimated data by employing the theory of basic reproduction number and by running the sensitivity analysis. Numerical simulation of the model was executed by using MATLAB to explore the outcome of certain key parameters when changes are applied on them.
VL  - 4
IS  - 5
ER  -

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