The invention of highly active antiretroviral treatment (HAART) revolutionalized the treatment of HIV and brought hope to millions of individuals living with the virus. However, the eradication of HIV has proved difficult owing to many factors including accessibility and treatment compliance, particularly among many individuals in low income countries. Thus, we developed a model in terms of a system of nonlinear ordinary differential equations to assess the influence of inaccessibility of treatment and noncompliance with treatment guidelines by the HIV infectives who are aware of their status on the spread of HIV. The model was studied qualitatively and quantitatively using the theory of reproductive ratio and the software Maple respectively. The results of the analysis showed that early detection, treatment accessibility and treatment compliance by the majority of the infectives who know their status are crucial to the minimization of HIV incidence and prevalence.