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Dynamical Analysis of Ratio-dependent Predator-Prey Models with Prey Refuge and Optimal Harvesting on Both Populations

 In this article, we discuss a dynamical analysis of ratio-dependent response predator-prey model with prey refuge and harvesting on both populations. Harvesting on predator and prey is used because both populations are assumed to have an economic value. In this model, it is also assumed that prey has an instinct to protect themselves from the threat of predators. The conducted dynamical analysis consists of determination of equilibria, existence conditions and their stability. Analytical results show that there are two equilibria: namely predator extinction point and the coexistence point which are exist and stable under certain condition. Furthermore, Pontryagin maximum principle is used to find optimal harvesting on predator and prey. Some numerical simulations are performed to illustrate the analytical result.