The most sensitive indicator of the health of a community is the infant mortality rate (option 2). This rate measures the number of deaths of infants under one year old per 1,000 live births in a specific period.

Option 1, the birth rate, refers to the number of live births in a population, which does not necessarily reflect the health of the community.

Option 3, the death rate, measures the number of deaths per 1,000 people in a population over a specific period. While it provides some insight into community health, it does not specifically focus on the health of infants.

Option 4, maternal mortality rate, measures the number of maternal deaths related to childbirth per 100,000 live births. While important for assessing maternal health, it does not solely reflect the health of the entire community.

Therefore, option 2, the infant mortality rate, provides the best indication of the overall health of a community, particularly in terms of the well-being of its youngest members.