| dc.description.abstract | Current treatment regimens have been effective in suppressing the progression of HIV. They prevent transmission and support people living with HIV to lead healthy lives. However, there are numerous clinical, social, and structural reasons that make people stop their treatment. HIV can re-surge after the treatment is stopped, which can also contribute to drug resistance and prevent further treatment. This is one reason why the search for an HIV cure is still essential for global public health. One major obstacle to developing a cure for HIV is the presence of what is called latent HIV reservoirs in the body. While CD4+ T-cells (one type of immune cell) are the most widely recognized reservoir, macrophages (another type of immune cell) have also been shown to contribute to the HIV reservoir. This thesis provides two novel mathematical models to understand the role macrophages play in the development of HIV pathogenesis. Both models start out with a reservoir of infected macrophages and the absence of infected CD4+ T-cells, reflecting the scenario where an individual with HIV stops treatment and that treatment has been fully effective in eliminating infected CD4+ T-cells. The two models differ in how the virus spreads, also called a transmission route. To focus solely on the role of macrophages, the first model only considers infections caused by macrophages. On the other hand, the second model also takes into account the transmission route between CD4+ T-cells. We study the stability of both systems around equilibrium points. This helps us know whether the disease would die out or establish itself and propagate further in the body. In both models, we have shown that a stable productive equilibrium point is attained under certain conditions. This proves that macrophages can indeed be a source of HIV persistence, which in turn undermines the importance of further study on macrophages for the ultimate goal of finding an HIV cure. | eng |