The long-term persistence of Mycobacterium tuberculosis in communities with high tuberculosis prevalence is a serious problem aggravated by the presence of drug-resistant tuberculosis strains. Drug resistance in an individual patient is often discovered only after a long delay, particularly if the diagnosis is based on current culture-based drug sensitivity testing methods. During such delays, the patient may transmit tuberculosis to his or her contacts. Rapid diagnosis of drug resistance would be expected to reduce this transmission and hence to decrease the prevalence of drug-resistant strains. To investigate this quantitatively, a mathematical model was constructed, assuming a homogeneous population structure typical of communities in South Africa where tuberculosis incidence is high. Computer simulations performed with this model showed that current control strategies will not halt the spread of multidrug-resistant tuberculosis in such communities. The simulations showed that the rapid diagnosis of drug resistance can be expected to reduce the incidence of drug-resistant cases provided the additional measure of screening within the community is implemented.