@ Spike-A-Pike
As far , as I am concerned , the British are not so much into eating freshwater fish as we continental Europeans , nothing to wonder about , since there is no place in the country much further away from the sea as approx. 120 miles(if I hazard a guess) .
At least during my various vacations over there in Oxfordshire in my teenage years I have never had those delicious "Fish and Chips" made of carp


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I fear , that there hardly are any means to get rid of those aliens in your local waters

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There are many different examples , that elsewhere all efforts to remove alien animals out of a native ecological system have failed so far .
With only rod and reel you would not be able to minor the stock of these fish significantly

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I don't know , how things are handled in the USA , but here in Germany the bigger lakes are in the hands of professional fishermen , these have the fishery rights in that waters hired from the owners(most likely state or county)and take care of the fish stocking and catching , also issue licenses for angling .
They make their living on these lakes and sell the , off course net-caught , fish to restaurants and on markets , partly also market them in own shops .
They surely would not overfish those waters , since they need to keep up their living also in the years to come .
What I mean to say is , that only such a professional fishing , employing all possible methods according to the target species , can minor your problem , but not entirely eliminate it

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Off course those netting and electric methods must be set up in a way not to affect other species too much , which also would be a problem !
It would propably be very costly to do , since it won't pay off , because you obviously do not have a market big enough for carp and snakehead in America .
An export to countries , that do have a market , would probably be too costly as well , therefore economically useless .
So maybe , all of you would have to change your habits about consuming fish(surely you could make fish fingers or burgers out of 'em , too) and set up an intensive fishery

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The Europeans have managed to render the Baltic and North Sea almost fishless , so you'd should manage with your lakes as well !
Another , very drastic , method would be to poison the entire water with a biodegreable poison to render it biologically dead and after a recreation time stock it again with native fish


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But as said before , its too drastic , and surely can't be done against the publics environmental conscience nowadays .
And it is also very unsave , since the aliens would always get back in somehow , since not all waters around can't be handled that way at the same time , because they are needed to provide a new stock of native fish .
No , only extensive net ,- or electric fishing could result into far less numbers of such alien fish , but if no market for human consumption somehow could be raised , who would pay for it

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Or are there already technologies developped , that could make fuel out of fish

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They can do it with corn , wheat and sugarcane.................

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Just a few thoughts from afar ,
good luck

, diemai