how does arthur not give everyone else TB?

ok so arthur somehow got TB from a very brief encounter with mr downes but somehow mrs downes and their son don't get it after living in the same house as mr downes? and then arthur doesn't spread it to anyone (as far as i know, i haven't completely the epilogue yet) despite having considerably longer proximity to other members of the gang than he ever did with mr downes?? is TB only contagious at like certain stages?? it doesn't make sense to me