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In this paper, we have studied the dynamics of two species, ecological model, considering two economically beneficial marine species herring ( Clupea harengus ) as predator and mysida ( Hemimysis anomala ) as its prey with Beddington–DeAngelis functional response, the effect of prey refuge and linear harvesting in both populations. The local and global stability of the equilibrium points has been established here. The axial equilibrium point goes through transcritical bifurcation depending on the harvesting effort of both species. The interior equilibrium point goes through super critical Hopf bifurcation depending on prey intrinsic growth rate. Additionally, we have determined the suitable value of the MSY policy for the harvesting and find suitable harvesting level using the optimal control theory, such that both the species persist simultaneously. Finally, numerical simulations have been performed to justify the theoretical findings. It is clear from the numerical simulations that the prey refuge and mutual interference between predators stabilized the unstable system to a stable one. This finding could give some clue to the experimental biologist and business personnel for making management decisions in controlling the harvesting strategies of the two economic beneficial fish populations, mysida and herring.

On optimal harvesting policy for two economically beneficial species mysida and herring: a clue for conservation biologist through mathematical model