There is increasing recognition that reinfection is an important component of TB transmission. Moreover, it has been shown that partial immunity has significant epidemiological consequences, particularly in what concerns disease prevalence and effectiveness of control measures. We address the problem of drug resistance as a competition between two types of strains of Mycobacterium tuberculosis: those that are sensitive to anti-tuberculosis drugs and those that are resistant. Our objective is to characterise the role of reinfection in the transmission of drug-resistant tuberculosis. The long-term behaviour of our model reflects how reinfection modifies the conditions for coexistence of sensitive and resistant strains. This sets the scene for discussing how strain prevalence is affected by different control strategies. It is shown that intervention effectiveness is highly sensitive to the baseline epidemiological setting.