An example is sea lamprey. When you say “success” you're inferring that we were able to eradicate and remove it. Regrettably, that doesn't happen.
Most of these organisms are highly successful, so instead we are able to control them. Through an annual investment of about $25 million there has been a lot of science on different control strategies. This has allowed lake trout, lake whitefish, and other species fisheries to recover. Within a decade of sea lamprey being detected in the Great Lakes, the fisheries collapsed totally, with reductions of 95%. We have now seen the return of fisheries and have actually declared rehabilitation—so it's a total success.
But rather than saying we successfully eradicated the invasive, we've successfully managed the invasive, but it came at a tremendous cost.