TB disease - treatment and infection
First there is one major difference between HIV and TB: As long as the TB bacteria are still susceptible to treatment (which is developing into a major problem in some regions of the world) there is a effective treatment which can eradicate the infection. For HIV this is not possible. Here we can only lower the viral load (sometimes under the detection limit), but when the treatment is stopped, the virus will return.

Then it seems that patients under treatment of a drug susceptible TB are infectious for a longer time than previously thought. Until now they have been isolated at the beginning of the treatment (typically around the first two weeks) until three consecutive sputum samples had been negative. Then they were released from isolation and thought to be non-infectious. At this point they are not cured, the treatment has to go on for several weeks.

Now there is newer research indicating that patients can still be infectious although they are under treatment and have negative sputum samples. It seems here that the currently used detection method is not sensitive enough. See these references for more information:


How Many Sputum Culture Results Do We Need To Monitor
Multidrug-Resistant-Tuberculosis (MDR-TB) Patients during Treatment?
High incidence of tuberculosis, low sensitivity of current diagnostic
scheme and prolonged culture positivity in four colombian prisons. A
cohort study.
Prolonged infectiousness of tuberculosis patients in a directly
observed therapy short-course program with standardized therapy.