As explained in the eNotes "Introduction" to Julius Caesar in the Study Guide:
Probably written in 1599, Julius Caesar was the earliest of Shakespeare's three Roman history plays. Like Antony and Cleopatra and Coriolanus, Julius Caesar is a dramatization of actual events, Shakespeare drawing upon the ancient Roman historian Plutarch's Lives of Caesar, Brutus, and Mark Antony as the primary source of the play's plot and characters.
Shakespeare was dependent upon Plutarch in translation for virtually everything he included in his play Julius Caesar. In The Life of Julius Caesar, Plutarch provides a great deal of information which explains Caesar's character. For example:
Now, at his love of danger his men were not astonished, knowing his ambition; but that he should undergo toils beyond his body's apparent powers of endurance amazed them, because he was of a spare habit, had a soft and white skin, suffered from distemper in the head, and was subject to epileptic fits, a trouble which first attacked him, we are told, in Corduba. Nevertheless, he did not make his feeble health an excuse for soft living, but rather his military service a cure for his feeble health, since by wearisome journeys, simple diet, continuously sleeping in the open air, and enduring hardships, he fought off his trouble and kept his body strong against its attacks.
It would appear that Caesar's personality and amazing military conquests resulted from his compensation for his physical afflictions. He drove himself relentlessly. As a general he achieved more than any other Roman general before or after him. Plutarch says that during the military part of his career he was responsible for the deaths of a million men. Shakespeare could hardly ignore Caesar's physical problems, since they were at least partly the cause of his great successes.
Caesar was tremendously ambitious and had tremendous will power. Shakespeare used Caesar's strong will to convey the theme that he was still powerful even after he had been assassinated. Brutus and Cassius could not prevail against Caesar's powerful will. In Shakespeare's play, both Brutus and Cassius acknowledge in their dying words that they were overcome, not so much by Antony and Octavius, as by the spirit of Julius Caesar. This explains why Shakespeare was able to title his play The Tragedy of Julius Caesar, even though he dies early in the third act, rather than titling the play "The Tragedy of Brutus," as critics have frequently suggested.
Shakespeare refers to Caesar's epilepsy, or "falling sickness," in Act I, Scene 2:
He fell down in the market-place, and foamed at
mouth, and was speechless.
'Tis very like: he hath the failing sickness.
No, Caesar hath it not; but you and I,
And honest Casca, we have the falling sickness.
I know not what you mean by that; but, I am sure,
Caesar fell down. If the tag-rag people did not
clap him and hiss him, according as he pleased and
displeased them, as they use to do the players in
the theatre, I am no true man.
In The Life of Antony, Plutarch describes Caesar's behavior during the festival of the Lupercalia, but does not mention his having an epileptic seizure at that time, although he does tell how Antony offered him a sort of crown on that occasion, as Casca tells Brutus and Cassius in Act I, Scene 1. Although Shakespeare borrowed heavily from Plutarch's Lives, he also dealt freely with the information he obtained.