Wasike, Silas Were2025-07-252025-07-252025-09https://ir-library.ku.ac.ke/handle/123456789/30833A research project submitted in partial fulfilment of the requirements for the award of the Degree of Master of Science in Applied Mathematics in the School of Pure and Applied Sciences of Kenyatta University, September 2024 Supervisor: Prof. James GatotoOverfishing and predation are causing loss of species in most fisheries worldwide and now most endemic fish species are on the brink of extinction. This threatens biodiversity and sustainability of these fisheries. Despite the many mitigation measures by the Kenyan government to address the decline of fish species in Lake Victoria, the decline continues unabated. A major decline has been observed in haplochromines (fulu) due to predation by Nile perch (mbuta) and the species is now in danger of extinction. There is need for research to enrich conservation practices for the fishery. To understand the preypredator dynamic system of the Nile perch and haplochromines, we have formulated and analyzed a two species prey-predator conservation model with a reserve area and prey refuge. The model is formulated using a logistic nonlinear differential equation which describes a self-limiting growth of a biological population and incorporates Holling type II functional response of the predator towards the prey. The fishery ecosystem is divided into two zones, the protected reserved area and the unreserved area. Scaling down the parameters of the equations was done to reduce the number of parameters for easier analysis of equilibrium points. The study aims to determine the positivity and boundedness of the model, the stability of equilibrium points, conditions for their existence and the effect of a reserve area on the stability of the system. Analysis of the model has been done, equilibrium points and conditions for their existence determined. The stability of equilibrium points both locally and globally has been established. To assess the effect of a reserve area on stability of the population of the system, numerical simulations in MATLAB using known parameters was done. This was done by variation of some parameters and the time series solutions drawn. The results showed that the reserved area has a stabilizing effect on the prey-predator dynamic systemenThesis