Abstract
Some of the biological species like tiger, deer and monkeys in Sundarbans, the largest mangrove forest in the world have been driven to extinction due to several external forces such as illegal poaching, over exploitation, predation, environmental pollution and mismanagement of habitat.This paper deals with a ratio-dependent predator-prey model with prey refuge and illegal harvesting of both species.The boundedness of solution, feasibility of interior equilibria have been determined. Optimal control technique has been applied to investigate anti-poaching patrol strategy for controlling the threat in the predator prey system facing in Sundarbans. The system is also examined so that the better control strategy is achieved. Moreover, the control strategy is obtained on the effect of variation of prey refuge. (C)2020 L&H Scienti fic Publishing, LLC. All rights reserved.