Browsing by Author "Lubangakene, Geoffrey"

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    Optimal harvesting of nile perch, nile tilapia, and small pelagic fish populations on lake Albert, Uganda
    (Muni University, 2025-11-10) Lubangakene, Geoffrey
    In this dissertation, an optimal fish harvesting problem for harvesting small pelagic fish, Nile tilapia, and Nile perch within a food chain, modelled with constant yield and constant effort harvesting, is considered. In particular, the optimal harvesting strategy that ensures both economic benefits and ecological sustainability of fish species was determined. The models were based on nonlinear ordinary differential equations that account for logistic growth, harvest, and species interactions. The problem is motivated by the need to address the concern of decreasing fish populations, resulting from overfishing and unsustainable harvesting practices. The optimality system, comprising the state equations, adjoint equations, and optimality condition, was derived using Pontryagin’s maximum principle. A forward-backward sweep method based on fourth-order Runge–Kutta schemes was employed to solve the optimality system. Peano’s existence theorem and Lipschitz uniqueness theorem were used to prove the existence and uniqueness, respectively, of solutions to the state equations. Numerical results show that for constant yield harvesting, harvest rates remained constant throughout the simulation period, with the highest harvest rate recorded for Nile perch and the lowest for Nile tilapia. In contrast, under constant effort harvesting, the highest harvest rate is again recorded for Nile perch, while the lowest is for small pelagic fish. Constant effort harvesting strategies allow fish populations to adjust dynamically and support ecological resilience. Whereas, constant yield harvesting risks over exploitation with any slight increase in harvest rates above the optimal level. The study recommends optimal harvesting strategies for Lake Albert, Uganda, as they promote ecological sustainability by preventing both over exploitation and underutilisation of resources. Fisheries managers should maintain fish populations at a moderate level by enforcing zero harvests when fish biomass is low to ensure faster recovery and reduce the risk of species extinction.