The classical age was rife with plague and disease. After all, the ancient world very often chalked up illnesses to the whims of capricious gods; and when you consider that there were open sewer systems, deplorable hygiene practices, not to mention a severe lack of penicillin, getting sick and dying weak and infirmed was par for the course.
Rulers, while able to afford a better quality of living, were not immune from disease.
From the Greek world: the statesmen Pericles was claimed by the Plague of Athens in the late 5th century BC.
It has long been believed that Julius Caesar was epileptic. Caesar’s abilities were greatly deteriorated by his sickness. It is said he collapsed while on campaign in Cordoba, Spain in 46 BC. Enfeebled by his sickness, Caesar also caused a public scandal when he refused to stand when the Senate was honoring him.
N.B. a new hypothesis states that Caesar actually suffered from mini-strokes, not seizures.
However, Rome’s first dictator perpetuo was not the only imperial ruler to succumb to illness.
It has long been suspected that Nero (37-68 AD), the supposed fiddle player, was mentally unfit for to hold the seat of power. It’s been suggested that he suffered from Histrionic personality disorder, a sickness characterized by excessive attention-seeking behavior.
Claudius
Gratus proclaims Claudius emperor
by Lawrence Alma-Tadema
Emperor Claudius (10 BC- 54 AD) had remarkably poor health that lead to unsightly behavior and paranoia. Polio has been suggested as a possible diagnosis. The historian Suetonius writes how…
…his laughter was unseemly and his anger still more disgusting, for he would foam at the mouth and trickle at the nose; he stammered besides and his head was very shaky at all times, but especially when he made the least exertion.

-Suetonius (Lives of the Twelve Caesars)

 
And then there’s Caligula.
Worst-Case Scenario
 
When considering the possible impacts of poor health of a ruler, Caligula certainly takes the cake as a worst-case scenario.
Seneca the Younger claimed Caligula (12-41 AD) possessed “monstrous cruelty”. It is reported that he killed on a whim; detaching heads from bodies of anybody who had ever crossed or disagreed with him.
“How is it that a young emperor, who was initially beloved by all, turned into one of histories most infamous loons?”
During a gladiator games, they ran out of criminals to throw into the arena. So Caligula ordered his guards to haul spectators into the ring to be eaten by lions.
A citizen once insulted Caligula. As punishment, the emperor ordered the man to be beaten with chains every day. The punishment was carried out for three months before the man was eventually beheaded.
In addition to his penchant for needless murder, Caligula is accused of other odd conduct.
It is said he publically had sex with his three sisters at banquets, sometimes on the table while the food was being served. He turned the imperial palace into a brothel. He also appointed his favorite horse, Incitatus, as a priest.
Caligula didn’t just take a page from the crazy book, he might have written the entire corpus.
What was the source of his madness? How is it that a young emperor, who was initially beloved by all, turned into one of histories most infamous loons?
For the first seven months of his reign, all adored him. Then, in 37 AD, the emperor became exceedingly ill. While Caligula made a full recovery, ancient writers report that he was never the same. His dire sickness seems to have either caused, or was at least preceded, by his monstrous killings and bizarre behaviors.
…it was not long before Gaius-who was now looked upon as a saviour and benefactor, and who was expected to shower down some fresh and everlasting springs of benefits upon all Asia and Europe, so as to endow the inhabitants with inalienable happiness and prosperity, both separately to each individual and generally to the whole state-began, as the proverb has it, at home, and changed into a ferocity of disposition.

-Philo of Alexandria (On the Embassy to Gaius)

So…. how important is the health of a ruler?
Well, maybe more than you think.