Ecological System of a Prey-Predator Model with Prey Reserve

: In this paper, we propose and analyze a mathematical model to study the dynamics of a fishery resource system in an aquatic environment that consists of two zones, a free fishing zone and a reserve zone where fishing is strictly prohibited. The existence of biological system is discussed. The local and global stability analysis has been carried out. An optimal harvesting policy is given using Pontryagins Maximum Principle.