A Prey Predator Conservation Model for a Fishery with a Reserve Area and Prey Refuge: A Study of Lake Victoria
Silas Were Wasike *
Department of Mathematics and Actuarial Science, Kenyatta University, P.O. Box 6 Malava Kenya.
*Author to whom correspondence should be addressed.
Abstract
The loss of species in most fishery ecosystems worldwide has reached crisis levels driven by habitat loss, overfishing, invasive species predation and climate change. This threatens biodiversity and sustainability of these fisheries. In Lake Victoria a major decline has been observed in haplochromines due to predation by Nile perch and the species is now in danger of extinction haplochromines are important to the lake because the feed on algae preventing algal bloom. In this paper a prey-predator conservation model for a fishery with a reserve area and prey refuge has been formulated using a logistic nonlinear dierential equations. The model incorporates Holling type II functional response of the predator towards the prey. In this research we study and analyze the stability of the prey-predator dynamic system of Nile perch (predator) and haplochromines (prey) in Lake Victoria. The lake ecosystem is divided into two parts, the reserve area and unreserved area. Equilibrium points have been determined and their local and global stability established by use of eigen value approach, Bendixon-Dulac criterion and lyapunov function. The eect of the reserve area and prey refuge on the stability of the system has been determined by simulation in MATLAB. Results show that a reserve area makes the system stable, and for certain values of migration rate 0:3 the population of the predator can coexist with prey.
Keywords: Prey predator, conservation model, mathematical model, equilbrium points, stability analysis