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This paper deals with the problem of selective harvesting in a hybrid type of prey-predator model. Here we have taken the fishing effort as a dynamic variable and tax as a control instrument. The existence of the possible steady states along with their local stability is discussed. The optimal tax policy is also discussed with the help of Pontryagin's maximum principle. Finally, two numerical examples are taken to illustrate some of the key results.

This paper describes a prey-predator model with Holling type II functional response incorporating constant prey refuge and harvesting to both prey and predator species. We have analyzed the boundedness of the system and existence of all possible feasible equilibria and discussed local as well as global stabilities at interior equilibrium of the system. The occurrence of Hopf bifurcation of the system is examined, and it was observed that the bifurcation is either supercritical or subcritical. Influences of prey refuge and harvesting efforts are also discussed. Some numerical simulations are carried out for the validity of theoretical results.

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A dynamic model for a single species fishery with stage structure is proposed using taxation as a control instrument to protect the fish population from overexploitation. Criteria for local stability and global stability of the system are derived. The optimal tax policy is established by using Pontryagin's maximal principle. By numerical simulation, it is shown that the fishery resources can be protected by increasing the tax.