Seven years ago, a deadly epidemic called "blood veil" swept through Korvosa, far beyond the ability of the city's clerics and paladins to heal the thousands infected. Roughly 2,200 of Korvosa's population of 18,500~ dead, leaving Korvosa worse than decimated. The affluent and the influential were, of course, among those who could afford to pay for healing, and so the victims of the disease came disproportionately from the impoverished, the disenfranchised, and the ethnic minorities like the Varisians and the Shoanti.
The Queen declared a quarantine of one of the poorest neighborhoods, overcrowded Old Korvosa, destroying all wooden bridges to the district and blockading the one remaining stone bridge, effectively consigning all within the district to dying of blood veil, leading to riots.
Though the Queen has since been deposed, Old Korvosa has turned away from the traditional authorities and Korvosa's established religions, distrusting them due to the former's terrible treatment and the latter's absence of support.
You may, if you so wish, incorporate this into your character's backstory. Perhaps they were a survivor of blood veil, perhaps they lost someone to blood veil. Perhaps they were a relative or are otherwise connected to the heroes that saved Korvosa seven years ago (the player characters of Curse of the Crimson Throne).
It is worth noting that while options that cure disease would be flavorful in light of such a backstory, that the `nightmare plague` of The House on Hook Street does not function as a disease under the rules. While such choices will not be useless, they are unlikely to see play more than once or twice over the course of the adventure.