A mathematical model for harvesting in a stage-structured cannibalistic system

Abstract

To increase the production of proteins in East Africa, aquaculture gained increased attention recently. In this paper, we study the interactions of a consumer-resource system with harvesting, in which African Catfish (Glarias gariepinus) consume a food resource. The cannibalistic behavior of African Catfish is captured by using a four stage-structured system. The dynamics of food resource and African Catfish result in a system of ordinary differential equations called a stage-structured fish population model. Existence and stability of steady states are analyzed quantitatively. We have investigated eight different harvesting scenarios which account for yield of the fish stock. Results from the simulations revealed that harvesting large juveniles and small adults under equal harvesting rates gives the highest maximum sustainable yield compared to other harvesting scenarios. In contrast to non-cannibalistic models, we find an increase of the proportion of the adult individuals under harvesting.