Dynamical analysis and optimal control in a hybrid stochastic double delayed bioeconomic system with impulsive contaminants emission and Lévy jumps.

•A hybrid stochastic double delayed system with impulse and Lévy jumps is proposed.•Combined dynamic effects of impulse, time delays and Lévy jumps are investigated.•Sufficient conditions for persistence in the mean and extinction are investigated.•The asymptotical stability in distribution of the proposed hybrid system is studied.•Optimal price control and maximum of expectation of sustainable yield are discussed.