Mathematical modeling of Fish Resources Harvesting with Predator at Maximum Sustainable Yield

Abstract

In this study, the population dynamic of fish is considered following Logistic model with the inclusion of harvesting. The prey-predator interaction is also considered with an assumption that the predator population which is completely theoretical and not physically defined has a little effect on the growth of prey population provided that there are no limiting factors other than the predators. This is to say that the prey-predator cycle remains stable as far as other factors are constant in the natural environment. The growth function of the predator population is constructed corresponding to the prey population, and its results showed that the predator population size is either convergent to a finite positive limit, zero or diverges to positive infinity; while the fish population size follows Logistic function and grows to an upper asymptote. Furthermore, the prey-predator interaction is considered with the assumption that the predator population has an effect on the growth of the prey population and the predator population has intra-specific competition for a limited environmental resource. Its result showed that both the prey- predator population size settle down to their corresponding coexistence equilibrium point.In both cases the maximum sustainable yield is obtained, numerical simulation and stability analysis of the model are included.

Keywords: Fish harvesting, Logistic model, Prey-predator, Koya-Goshu, Numerical simulation, Stability analysis, Maximum sustainable yield.