Human has been successful in the eradication of species as the moa or the dront. The war against mosquitoes started in the beginning of the 20th century and more effort has been put in it than in any other eradication project. Still it has not been very effective. Sardinia was practically covered with DDT after WWII, but it is not unusual to stumble on Anopheles labranchiae there again.
Malaria has been eradicated from 79 countries. In all but the Maldives and Palestine we have “Anophelism without malaria”. Also on the Maldives and in Palestine the vector was eradicated later than the disease. Personally I think that vector control is essential for fighting annual malaria cases and local epidemics, but history shows that it won’t lead to malaria eradication.