It does come up, just not very often:
I think that there are periodic outbreaks of disease that flourish in the environs, same as any other medieval city. I just think that GRRM hasn’t devoted any wordspace to the idea, because unlike real life, GRRM has editors and a word count.
Thanks for the question, Leon.
SomethingLikeALawyer, Hand of the King
“Dunk had heard that, too. “Were you there during the Great Spring Sickness?”
“Oh, indeed. A dreadful time, ser, dreadful. Strong men would wake healthy at the break of day and be dead by evenfall. So many died so quickly there was no time to bury them. They piled them in the Dragonpit instead, and when the corpses were ten feet deep, Lord Rivers commanded the pyromancers to burn them. The light of the fires shone through the windows, as it did of yore when living dragons still nested beneath the dome. By night you could see the glow all through the city, the dark green glow of wildfire. The color green still haunts me to this day. They say the spring was bad in Lannisport and worse in Oldtown, but in King’s Landing it cut down four of ten. Neither young nor old were spared, nor rich nor poor, nor great nor humble.” (Sworn Sword)
"Ser Jaime, I have seen terrible things in my time,” the old man said. “Wars, battles, murders most foul … I was a boy in Oldtown when the grey plague took half the city and three-quarters of the Citadel. Lord Hightower burned every ship in port, closed the gates, and commanded his guards to slay all those who tried to flee, be they men, women, or babes in arms. They killed him when the plague had run its course. On the very day he reopened the port, they dragged him from his horse and slit his throat, and his young son’s as well. To this day the ignorant in Oldtown will spit at the sound of his name, but Quenton Hightower did what was needed. Your father was that sort of man as well. A man who did what was needed.” (AFFC, Jaime I)
“We held the city today, my lord, but I make no promises for the morrow. The kettle is close to boiling. So many thieves and murderers are abroad that no man’s house is safe, the bloody flux is spreading in the stews along Pisswater Bend, there’s no food to be had for copper nor silver. Where before you heard only mutterings from the gutter, now there’s open talk of treason in guildhalls and markets.” (ACOK, Tyrion IX)