Possible Clues:

• Always present to kill the mice in bits
• If they're ever-present, finish the mice by cutting them in bits
• Peculiar, you conclude, to a certain variety of mice
• Disease found locally is one to be eliminated by distribution of medicine
• Finish off mice scattered throughout a neighbourhood
• Flu to die out, given experiment with mice?
• Experimental medicine Italy once dismissed is confined to a particular area
• Prevalent
• Limit spread of mice in a particular area
• Either one leaving medicine out in local