Devastatingly, in spite of the long standing research works on HIV/AIDS infection and treatment dynamics, reviews of existing models clearly shown that the behavioral attitude to treatment consistency by those screened to become aware and those receiving treatment have not been given the desired attention. Moreso, the inconsistency following avoidable treatment truncation and later resumption of treatment by these classes of infectives, which could lead to colossal drug abuse is also not accorded the much expected consideration. Therefore, in this present study, we sought and formulated a nonlinear 6-Dimensional deterministic mathematical HIV/AIDS dynamic model that accounted for the global stability analysis of the role of antiretroviral therapy abuse for the treatment of HIV/AIDS epidemic. The model is structured upon dynamical interactions between 6-subpopulations and HI-virus under bilinear control functions with constant screening of the susceptible. It is assumed that the rate of resumption of ART upon truncation is less than initial ART truncation following the incorporation of HIV aware infectives not ready to receive ART treatment and HIV aware infectives with truncated treatment protocol The system mathematical well-posedness was investigated and model reproduction number determined for both off-treatment (with value 0.343 ) and for onset-treatment (with value 0.271). We considered the model for off-treatment and thereafter by incorporating LaSalle's invariant principle into classical Lyapunov function method, we presented an approach for the global stability analysis of the role of ART abuse in HIV/AIDS treatment. Furthermore, the analysis and results of this paper presented a dynamic methodological application of bilinear control functions and an impeccable understanding of the fundamental mechanism in HIV/AIDS treatment in the presence of ART abuse. Using in-built Runge-Kutta of order of precision 4 in a Mathcad surface, numerical validity of model is conducted to investigate the study theoretical and analytical predictions. Results shows that application of onset-treatment functions with trend of ART abuse yield tremendous reduction in HIV/AIDS infection epidemic following the recovery rate of the susceptible population with value increasing from 0.5 cells/mm 3 to 1.203 cells/mm 3 within the first 3 months and attained stability of 0.62 cells/mm 3 through the time interval of 20-30 months.

From the studies of HIV/AIDS transmission and treatment dynamics using mathematical modeling, literature reviews have shown that attention had not been given to the behavioral attitude of screen-aware infectives not ready to receive treatment, HIV-aware infectives that initiated treatment but truncated only to resume treatment later (therapy abuse) and those on consistent treatment protocols. Moreso, following the non-outright eradication of the deadly HI-virus, recommendations have been geared towards exploring optimal control theory for the maximization of healthy uninfected CD4 + T-cells. Therefore, this present investigation seeks and formulated an optimal control 6-Dimensional deterministic mathematical dynamic model, which accounted for the Role of Antiretroviral Therapy (ART) abuse in the treatment dynamics of the HIV/AIDS epidemic. The materials and methods for this model are constituted by a set of 6-Dimensional varying subpopulations interacting with concentrated HI-viral load. Interactions are investigated using bilinear control functions (condom use and ART) with empirically generated data. The model assumed a deterministic approach and was formulated using the fundamental theory of differential equations. Theoretical optimal predictions explored classical numerical methods with optimal control techniques (Pontryagin's maximum principle in conjunction with Hessian matrix) as a basis. Numerical simulations were conducted using in-built Runge-Kutta of the order of precision 4 in a Mathcad surface. Following the derived model for both offoptimal control and onset-optimal control functions and model optimal control pair as well as model optimality system, results of simulations indicated that at off-optimal control function, near zero population extinction was observed. From the application of optimal control functions under optimal control techniques, there exists tremendous rejuvenation of susceptible populations vindicated by a reduction in the rate of ART abuse under a minimal proportion of bilinear control functions. The study concluded that adopting optimal control techniques for the investigation of the role of ART abuse in HIV/AIDS treatment yield highly significant recovery of healthy CD4 + T-Cells at minimal systemic cost when compared with off-optimal control outcome. Therefore, the study not only affirmed the vital concept of optimal control strategy but also, instituted the viability of the model. Thus, this model can be extensively used in Bio-system and applied mathematics.