Schematic stock and flow diagram of the susceptible-infected-treated-removed model. We adopted a deterministic, compartmental, susceptible-infected-treated-removed-susceptible (or SITRS) framework. The susceptible class, S, contained those who were sexually active and could become infected; the infected class, I, contained those who were infectious; the treated class, T, containing both true and false positives; these people were assumed to have been tested, diagnosed as cases, and treated appropriately; the removed class, R, contained those who had naturally recovered from infection, and those who were given a positive diagnosis and temporarily reduced their sexual risk-taking behaviour after being treated. People in the removed class were assumed to eventually exit the sexually active population, or return to the susceptible class as a result of waned immunity or relapse into previous risky sexual behaviour. Additional model structures that were also investigated are displayed in Additional file 1.