A Logistic Growth Model with Discrete-Time Delay and a Restriction on Harvesting

The paper examines the fish population dynamics of a delay logistic model with restrictions on harvesting in a deterministic environment. This is the first time an autonomous model with a harvesting function has been created to regulate the harvesting of fish. The goal of the study is to help external regulatory bodies manage fishing harvests and replenish fish stocks. The dynamics scenario mirrors the facts of fishing systems and enhances the research that has already been done. Two restriction conditions are employed. In the event that the agency detects overfishing, all fish harvesting is prohibited, with the fishing control parameter raised in order to bring the fish back to full stock, while the catchability coefficient is set to zero. However, if the system is designed so that harvesting is carried out in accordance with the fish’s sustainable growth level, then we have the partial restriction condition where no ban is imposed on fishing. This model’s practical benefit is its adaptability; it may be redesigned to suit any physical system whose functioning is comparable to this phenomenon. As a result, it is advised that the regulatory bodies use the model to manage the fish stock.