The dynamics underpinning our model are shown schematically in Figure 1 . Individuals are either susceptible (S), infectious (I) or traced (T) and move between these compartments due to four processes: infection; treatment; tracing; and stopping tracing. This paradigm is suitable for the consideration of sexually transmitted diseases, where infectious individuals can transmit infection to contacts, then seek treatment, which clears the pathogen and stops transmission but leaves the individual susceptible. It also involves the process of contact tracing, which we use as a general term that includes both partner notification and efforts by public-health workers to track down potentially infected individuals.