This study involves the mathematical modelling of long-term HIV dynamics and the investigation of optimal treatment strategies. In our previous work, we produced a model which replicates literature-reported clinical data from untreated patients with good agreement and is able to predict the entire trajectory of the disease. Here, we extend the model to account for therapy and the emergence of virus resistant to antiretroviral drugs. We compare the new model with clinical data and use it to investigate the effect of continuous and interrupted (structured treatment interruptions, STI) therapy. For the former, there exist optimal combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies for which both the wild-type (drug-sensitive) virus is depleted and the time at which mutated (drug-resistant) virus becomes dominant is extended. The simulation results also suggest that 'PI-based' drug regimes work better than 'RTI-based' ones. For STIs, there exists an optimised schedule of ON and OFF treatment by which the interplay between drug-sensitive and drug-resistant virus does not allow either of them to grow in an uncontrolled manner and deplete CD 4 + T-cells (the main target of HIV: they 'orchestrate' the immune response). Furthermore, the schedule minimises the impact of side-effects that may arise during therapy. The results show that an optimised schedule, facilitating the interplay between the two virus strains, is the key to the successful implementation of STIs, which have so far been unsuccessful in extending survival-time considerably. Whereas continuous therapy fails when treating patients that have developed strong drug resistance, STIs prove to be very promising. The simulation and optimisation results indicate that although complete eradication of the virus may not be possible, controlling it over a considerable length of time is feasible.