Final answer:
Anthrax caused by Bacillus anthracis is the bioterrorism agent that requires treatment with 60 days of continuous antibiotics.
Step-by-step explanation:
The bioterrorism agent that requires treatment with 60 days of continuous antibiotics is Anthrax caused by the bacterium Bacillus anthracis. Anthrax can be transmitted through inhalation, ingestion, or skin contact with the spores. Treatment involves antibiotics such as ciprofloxacin or doxycycline, which should be taken for a prolonged period of two months to ensure complete eradication of the bacteria.