Yes, there has been such a situation in which various parasites and microorganisms may need to be eradicated from the earth.

Scientists are working hard to eradicate this parasite as these insects are dangerous to human health and have succeeded in eradicating smallpox from Earth by successfully using vaccines.

This shows how people deliberately want to get rid of these kind of species.

Other programs aimed at eradicating Hepatitis B are vaccinated against polio, and other programs designed to eradicate these pests specifically.