Optimal Control of a Threatened Wildebeest-lion Prey-predator System Incorporating a Constant Prey Refuge in the Serengeti Ecosystem
Applied and Computational Mathematics
Volume 4, Issue 4, August 2015, Pages: 296-312
Received: Jun. 29, 2015; Accepted: Jul. 9, 2015; Published: Jul. 17, 2015
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Authors
Thadei Damas Sagamiko, Department of Mathematics, University of Dar Es Salaam, Dar Es Salaam, Tanzania
Nyimvua Shaban, Department of Mathematics, University of Dar Es Salaam, Dar Es Salaam, Tanzania
Cuthbert Leonard Nahonyo, Department of Zoology and Wildlife Conservation, University of Dar Es Salaam, Dar Es Salaam, Tanzania
Oluwole Daniel Makinde, Faculty of Military Science, Stellenbosch University, Stellenbosch, South Africa
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Abstract
In this paper a two species prey-predator model is developed in which prey is wildebeest and predator is lion and both are threatened by poaching, drought and diseases.The system is found in the Serengeti ecosystem.The model is constructed based on Holling type II functional response incorporating a constant prey refuge. We apply optimal control theory to investigate optimal strategies for controlling the threats in the system where anti-poaching patrols are used for controlling poaching, construction of dams for mitigating drought and vaccination for diseases control. The possible impact of using combinations of three controls either one at a time or two at a time on the threatened system plus a refuge factor is examined. All control strategies have shown significant increase in prey and predator populations . However, the best result is achieved by controlling all threats together. The effect of variation of prey refuge to the control of threats is studied and results indicate that increase of causes more prey individuals to be saved and reduces the number of predator individuals saved. This behaviour agrees with theoretical results obtained in co-existence equilibrium point.
Keywords
Optimal Control, Prey-predator System, Prey Refuge, Threat, Gregariousness
To cite this article
Thadei Damas Sagamiko, Nyimvua Shaban, Cuthbert Leonard Nahonyo, Oluwole Daniel Makinde, Optimal Control of a Threatened Wildebeest-lion Prey-predator System Incorporating a Constant Prey Refuge in the Serengeti Ecosystem, Applied and Computational Mathematics. Vol. 4, No. 4, 2015, pp. 296-312. doi: 10.11648/j.acm.20150404.18
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