@Roel The allmighty You’d be surprised, pulmonary tuberculosis mainly spreads through airborne droplets (released through coughs or sneezes) coming in contact with the eye or mouth. That’s why, although present pretty much everywhere, Tuberculosis was especially widespread in cramped, inhumane slums. The gang’s camps are quite hygienic, with much open space and Ms. Grimshaw monitoring. Additionally, Arthur always seem coughing into his arm.
However, I’m sure at least someone caught it, but it isn’t uncommon for the disease to remain dormant for many years, if not indefinitely (notice how Arthur never coughed or exhibited any symptoms until after Blessed Are the Peacemakers, where Arthur was strung up, malnourished and poisoned - perfect kind of traumatic experience that could weaken the victim’s immune system enough for TB to become dangerous).
Seriously, if every person who caught TB manifested the lethal symptoms, the human race would have died out a long time ago.