Comparatively, HIV like most viruses is very minute, unadorned organism which cannot reproduce unaided. It remains the most deadly disease which has ever hit the planet since the last three decades. The spread of HIV has been very explosive and mercilessly on human population. It has tainted over 60 million people, with almost half of the human population suffering from AIDS related illnesses and death finally. Recent theoretical and computational breakthroughs in delay differential equations declare that, delay differential equations are proficient in yielding rich and plausible dynamics with reasonable parametric estimates. This paper seeks to unveil the niche of delay differential equation in harmonizing low HIV viral haul and thereby articulating the adopted model, to delve into structured treatment interruptions. Therefore, an ordinary differential equation is schemed to consist of three components such as untainted CD4+ T-cells, tainted CD4+ T-cells (HIV) and CTL. A discrete time delay is ushered to the formulated model in order to account for vital components, such as intracellular delay and HIV latency which were missing in previous works, but have been advocated for future research. It was divested that when the reproductive number was less than unity, the disease free equilibrium of the model was asymptotically stable. Hence the adopted model with or without the delay component articulates less production of virions, as per the decline rate. Therefore CD4+ T-cells in the blood remains constant at 𝛿1/𝛿3, hence declining the virions level in the blood. As per the adopted model, the best STI practice is intimated for compliance. / Mathematical Sciences / Ph.D. (Applied Mathematics)

Current research on HIV therapy is diverse and multi-disciplinary. Engineers however, were late in joining the research movement and as such, engineering literature related to HIV chemotherapy is limited. Control engineers in particular, should have risen to the challenge, as it is apparent that HIV chemotherapy and control engineering have a lot in common. From a control theoretic point of view, HIV chemotherapy is control of a time varying nonlinear dynamical system with constrained controls. Once a suitable model has been developed or identified, control system theoretical concepts and design principles can be applied. The adopted control approach or strategy depends primarily on the control objectives, performance specifications and the control constraints. In principle, the designed control system can then be validated with clinical data. Obtaining measurements of the controlled variables however, has the potential to hinder effective control. The first part of this research focused on the application of control system analytical tools to HIV/AIDS models. The intention was to gain some insights into the HIV infection dynamics from a control theoretic perspective. The issues that needed to be addressed are: Persistent virus replication under potent HAART, variability in response to therapy between individuals on the same regimen, transient rebounds of plasma viremia after periods of suppression, the attainment, or lack thereof, of maximal and durable suppression of the viral load. The questions to answer were: When are the above mentioned observed responses to therapy most likely to occur as the HIV infection progresses, and does attaining one necessarily imply the other? Furthermore, the prognostic markers of virologic success, the possibility of individualizing therapy and timing the initiation of antiretroviral therapy such that the benefits of therapy are maximized, are matters that were also investigated. The primary objective of this thesis was to analyze models for the eventual control of the HIV infection. HIV therapy has multiple and often conflicting objectives, and these objectives had to be prioritized. The intention of the proposed control strategy was to produce practical solutions to the current antiretroviral problems. To this end, the second part of the research focused on addressing the HIV/AIDS control issues of sampling for effective control given the invasive nature of drawing blood from a patient and the derivation of drug dosage sequences to strike a balance between maximal suppression and toxicity reduction, when multiple drugs are concomitantly used to treat the infection. / Thesis (PhD)--University of Pretoria, 2006. / Electrical, Electronic and Computer Engineering / Unrestricted