Applied and Computational Mathematics
Volume 4, Issue 5, October 2015, Pages: 363-368
Received: Aug. 27, 2015;
Accepted: Sep. 8, 2015;
Published: Sep. 22, 2015
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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
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.
Frank Nathan Ngoteya,
Sensitivity Analysis of Parameters in a Competition Model, Applied and Computational Mathematics.
Vol. 4, No. 5,
2015, pp. 363-368.
Baigent, S., 2010. Lotka-Volterra Dynamics- An Introduction. [Online] Available at: http://www.ltcc.ac.uk/courses/BioMathematics/LTCC LV2010 [Accessed 8 4 2015].
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.
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.
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.
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].
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].
IUCN Red List, 2008. Endangered Species. [Online] Available at: http://www.iucnredlist.org/ [Accessed 27 May 2015].
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.
Mikucki, M. A., 2012. Sensitivity analysis of the basic reproduction number and other quantities for infectious disease models, Colorado: Colorado State University.
Nakayama, S. and Fuiman, L. A., 2010. Body size and vigilance mediate asymmetric interference competition for food in fish larvae, Oxford: Oxford University Press.
Painted Dog Conservation Incorporated, 2014. Threats. [Online] Available at: http://www.painteddogconservation.iinet.net.au [Accessed 28 May 2015].
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.
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.
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.