Abstract: In this paper, we consider a prey-predator fishery model with prey dispersal in a two-patch environment, one is assumed to be a free fishing zone and the other is a reserved zone where fishing and other extractive activities are prohibited. The existence of possible steady states of the system is discussed. The local and global stability analysis has been carried out. An optimal harvesting policy is given using Pontryagin's maximum principle.

Key words: prey-predator, global stability, optimal harvesting