Loss to follow-up (LTFU) is a serious problem in most sub-Saharan African ART programmes. If ART is interrupted or reduced, HIV again progresses, and this increases the risk of opportunistic infections and, ultimately, AIDS and death. In addition, the viral load of a patient who interrupts ART will rebound, and the probability of onward transmission increases. If tracing programmes can accelerate the return of lost patients, these patients may be less likely to transmit the virus, since the period of lapsed treatment is shortened. In this study, we created a mathematical model to determine whether tracing patients LTFU from ART programs would lower the rate of HIV transmission.