Final answer:
American citizens became interested in establishing government-controlled boards of health due to their fear of infectious diseases, the need for adequate funds for healthcare, and the importance of accurate records for public health planning.
Step-by-step explanation:
American citizens became interested in establishing government-controlled boards of health for multiple reasons. One reason was their fear of infectious diseases such as yellow fever. By establishing boards of health, the government could take measures to prevent and control the spread of these diseases, ensuring the safety and well-being of the citizens. Another reason was that such boards could tax and ensure adequate funds to pay for healthcare and other necessary services. Lastly, establishing these boards would allow for accurate records of births and deaths, providing valuable data for public health planning and research.