Modelling the effects of treatment on chronically infected HIV-positive patiants.

The devastating impact of HIV as a chronic infectious agent on humankind has forced a consideration of the rationale of administering combined drug therapies that incorporate fusion inhibitors, reverse transcriptase inhibitors and protease inhibitors in chronically infected HIV patients. It is also worth considering using alternative therapies, such as antioxidants, as anti-retroviral therapies are limited for economic reasons and their associated toxicity. This study models and analyzes pretreatment dynamics of viral production and progression with cellular-mediated immune responses in chronic HIV infection. The pre-treatment model is then extended to investigate the impact of administering a three drug combination regimen of reverse transcriptase inhibitors, protease inhibitors and fusion inhibitors to chronically infected HIV-positive patients. Again from the pretreatment model we develop that considers HIV-induced free radicals as promoters of apoptosis and viral replication, incorporating antioxidants as agents of oxidative defense against the the oxidative pressures caused by the free radical molecules in chronically infected HIV patients. Deterministic mathematical models of ordinary differential equations shall be used for the three models of the thesis. An analysis of the effects of the parameters of interest is done for each one of the three models described above. In particular, this analysis is going to be centered on the reproduction numbers, stability conditions for steady states and numerical simulations. Results from the three models show that cellular-mediated immune responses, both lytic and non-lytic, play a significant role in reducing the initial impact of HIV infection. Administering combined chemotherapy helps boost CD4 count and significantly reduce viral load in chronically infected HIV patients. This treatment strategy gives positive results especially if it can be applied with relatively high efficacy rate, which might require almost perfect adherence and compliance as well as a well balanced diet and a positive psycho-social lifestyle by infected individuals. Antioxidant supplements also have great potential as far as inhibition of viral replication and maintenance of T-cell viability and survivability in chronically infected HIV patients is concerned, especially when applied right from the onset of infection. Antioxidant supplements may serve as a better alternative to chemotherapy because they are non-toxic,affordable and do not present a problem of resistance as they need not be strain specific. It can also be deduced from the results of the antioxidant therapy models and the chemotherapy model that great clinical benefits can be realized by administering antioxidant supplements concurrently with combined drug therapy, a strategy defined in this thesis as complementary therapy