Abstract
A mathematical model is proposed and analysed to study the dynamics of two-prey one predator system of fishery model with Holling type II function response. The effect of harvesting was incorporated to both populations and thoroughly analysed. We study the ecological dynamics of the Nile perch, cichlid, and tilapia fishes as prey-predator system of lake Victoria fishery in Tanzania. In both cases, by nondimensionalization of the system, the equilibrium points are computed and conditions for local and global stability of the system are obtained. Condition for local stability was obtained by eigenvalue approach and Routh-Hurwitz Criterion. Moreover, the global stability of the coexistence equilibrium point is proved by defining appropriate Lyapunov function. Bioeconomic equilibrium is analysed and numerical simulations are also carried out to verify the analytical results. The numerical results indicate that the three species would coexist if cichlid and tilapia fishes will not be overharvested as these populations contribute to the growth rates of Nile perch population. The fishery control management should be exercised to avoid overharvesting of cichlid and tilapia fishes.
Highlights
In today’s life, the relationship between predator and prey became an important aspect to discuss in ecology
The current study considers lake Victoria fishery found in Tanzania as a case study
We have not gone to the field, but the current trends on the dynamics of species in the lake have been obtained from reading different literature such as NPFMP [2], FAO [3], LVFO [4], Barack [5], and Barilwa [6]
Summary
In today’s life, the relationship between predator and prey became an important aspect to discuss in ecology. We have not gone to the field, but the current trends on the dynamics of species in the lake have been obtained from reading different literature such as NPFMP [2], FAO [3], LVFO [4], Barack [5], and Barilwa [6]. This literature explains the current trend of the lake and the fishery management of the lake Victoria. The lake is comprised of a lot of species such as stocked Nile perch, Lates niloticus, tilapia fish, Oreochromis niloticus, the cyprinid, Rastrineobola argentea, catfishes, insects, cichlids, crocodiles, and many zooplanktons and phytoplanktons NPFMP [2]
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