After Caesar turned 50, he occasionally had seizures, during which he fainted and had muscular convulsions. Four of his attacks were documented as they occurred during official functions. This may have been epilepsy, which is more common in older people. Today, we have medications that prevent most seizures, but before modern medicine, the disorder was more noticeable and was known as the "falling sickness.”

Comparing the health of society and its government to that of the human body was a favorite metaphor of Shakespeare's. Here, Cassius is saying that it's Rome which is suffering from the "falling sickness," because the political health of the Republic has collapsed under the dictatorship of Caesar.