On non-selective harvesting of a multispecies fishery incorporating partial closure for the populations

- We describe a prey-predator fishery model incorporating partial closure for the populations.
- The criterion for the existence of interior equilibrium point, local and global stability of the system are derived.
- The existence of bionomic equilibrium is discussed.
- The optimal system is derived and solved numerically using an iterative method with Runge-Kutta fourth-order scheme.
- Numerical simulations are carried out to verify the analytically proved results.

A prey-predator type fishery model incorporating partial closure for the populations is described in this paper. The proposed model deals with a problem of non-selective harvesting of a prey-predator system in which both the prey and the predator species obey logistic law of growth. The predator dependent Beddington DeAngelis type functional response is taken into consideration. Dynamic behavior of the system is analyzed. Partial closure for the populations is considered as a controlling instrument to regulate the harvesting of the populations. A dynamic framework towards the optimal utilization of the resource is developed using Pontryagin's maximum principle. The optimal system is numerically solved using an iterative method with Runge-Kutta fourth order scheme. Simulation results show that the optimal control scheme can achieve sustainable ecosystem. Results are analyzed with the help of graphical illustrations.