Numerical simulations of inland fisheries mathematical models

Abstract

This research focuses on numerical simulations of the prey-predator mathematical model in inland fisheries. The problem of excessive harvesting results in unsustainable harvesting so fishermen will spend capital for restocking the fish population. Mathematical models can provide ideal harvesting effort calculations to obtain a sustainable harvesting strategy to reduce the cost of harvesting in the following period. Two mathematical models were created in this paper. The first model considered a condition in which there was no interaction between prey and predator, and the second model considered a condition in which there was interaction between prey and predator. The first model assumed that a juvenile fish population (x1) was introduced and grew into native adult fish (x2) and the native adult fish reproduced spawn fish (x3). The second model behaves like the first but adds a predatory fish population, and assumes it interacts with the introduced juvenile stock fish population (x1) and the spawn fish population (x3). Dynamic analysis of the mathematical models is carried out to obtain the equilibrium points and their stability analysis. Numerical simulations of both models were done using the Euler method to show that the maximum sustainable yield effort (EMSY) value influences the number of fish populations in inland fisheries because harvesting effort will maintain sustainable harvesting. The simulation suggests that if the harvesting effort is above the 2EMSY value, the fish population will approach the equilibrium point (0,0,0) in the first model and (0,0,0,0) in the second model. However, if the harvesting effort is less than or the same as the 2EMSY value, the fish population will approach the equilibrium point when adult fish and spawn fish exist in both models. In conclusion, determining harvesting efforts following the EMSY value is expected to support sustainable harvesting so that the economy of inland fishery can be sustainable.