Abstract
In this paper, a fishery model for African catfish and Nile tilapia is formulated. This model is used to compare financial profit and biomass outtakes in a two-species system versus single species systems. We consider a stage-structured fish population model consisting of the aforementioned fish species together with two food resources. The model dynamics include cannibalism, predator-prey, feeding, reproduction, maturation, development, mortality, and harvesting. We prove consistency of the model in the sense that the solutions will stay bounded and nonnegative over time. Conditions for local stability of fish-free equilibrium point are established. The simulation results reveal asymptotically stable solutions with coexistence of African catfish, Nile tilapia, and two food resources. The major conclusion from our findings is that fisheries should culture both species to maximize the biomass outtake and financial profit.
Highlights
Fish is a source of animal protein, providing many key nutrients and calories that are needed for physical and mental development [1, 2]
Our simulations are stable in the sense that when positive initial values are used, the solutions approach the positive steady state as indicated by Figure 3 which shows the dynamics of the solutions to system (18)
We present some of these properties, using equal harvesting in all stages in our model: Figure 4 for African catfish and Nile tilapia and Figure 5 Nile tilapia only
Summary
Fish is a source of animal protein, providing many key nutrients and calories that are needed for physical and mental development [1, 2]. Fish contribute 17 percent of animal protein and 7 percent of all proteins and are crucial for over 3 billion people in developing countries [3]. The fishery industry contributes to the gross domestic product (GDP) and has continued to be an important source of foreign exchange earnings through fish exports to the East African region and international markets [4]. Due to the importance of fish to so many people, the demand is very high and has resulted in overfishing and a decrease in fish population stock [5, 6]. There is a need to develop sustainable fisheries management practices in East Africa
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