Impact of Levels Taxation on Fisheries Management

Abstract

In this study, we present two stock-effort mathematical models for fishery management, governing four ordinary differential equations that describe the dynamics of the fish stock and the fishing efforts. The initial model pertains to constant displacement rates of fishing effort, while the second model involves displacement rates that depend on fish stock. The first two equations track the changes in two fish populations, which migrate and grow across two distinct regions and are subject to exploitation by two separate fishing fleets, each with its corresponding fishing effort. Assuming that the growth of fish and changes in fishing effort occur over a slower time scale, while fish migration and vessel movement take place over a faster time scale. Subsequently, an aggregation of variables approach is used to get an aggregated model. This aggregated model is analyzed mathematically. The influence of taxation on the population of fish and the income generated by the fishery is being investigated. Numerical simulations are showcased to demonstrate the results.