Recent development in antiretroviral treatment against HIV can help AIDS patients to fight against HIV. But the question that whether the disease is to be partially or totally eradicated from HIV infected individuals still remains unsolved. Usually, the most effective treatment for the disease is HAART which can only control the disease progression. But as the immune system becomes weak, the patients can not fight against other diseases. Immune cells are activated and proliferated by IL-2 after the identification of antigen. IL-2 production is impaired in HIV positive patients and intermitted administration of immune activator IL-2 together with HAART which is a more effective treatment to fight against the disease. Thus, its expediency is essential and is yet to be explored. In this article we anticipated a mathematical model of the effect of IL-2 together with RTIs therapy in HIV positive patients. Our analytical as well as numerical study shows that the optimal schedule of treatment for best result is to be obtained by systematic drug therapy. But at the last stage of treatment, the infection level raises again due to minimisation of drug dosage. Thus we study the perfect adherence of the drugs and found out if RTIs are taken with sufficient interval then for fixed interval of IL-2 therapy, certain amount of drug dosages may be able to sustain the immune system at pre-infection stage and the infected CD4(+)T cells are going towards extinction.