A spatiotemporal system of partial differential equations is implemented for describing a marine predator-prey system of shark and prey fish. The model is developed to account for predator migration and for harvesting of both predator and prey animals. The Finite Difference Method is employed to develop a numerical model to describe the behavior of the system in space over time. The dynamics of the system for different initial conditions for predator and prey populations and harvesting rates of both predators and prey using the numerical scheme. The resulting dynamics of the system from adding a predator sanctuary (an area within which the predator cannot be harvested) are also examined. It is hoped that this paper will illustrate that model behaves as a predator-prey system is expected to behave under the tested conditions.