|The viral dynamics model based on a system of differential equations is an incredibly useful tool towards understanding the kinetics of HIV. The parameters of the system of equations provide important insights into the dynamics of the infection and treatment of the disease, and have far reaching biological implications. It is almost impossible to directly measure these parameters experimentally, and thus our best option is often to estimate them through observed longitudinal viral load data. In this thesis I attempt to estimate these parameters in data on rhesus macaques infected with SIV (the gold-standard animal model of HIV infection) and treated with antiretroviral therapy as well as potentially a TLR7-agonist, a new immunotherapy that has promising potential to cure, during acute and rebound stages of infection using a maximum likelihood based fitting algorithm. The primary results of this thesis were in highlighting the limitations of attempting to simultaneously fit all seven parameters of the viral dynamics model. In the rebound stage of infection, the most precise parameter estimates arise when a subset of parameters are fixed based on prior knowledge, which can resolve issues of parameter non-identifiability. In terms of being able to ultimately determine biological implications such as the kinetics associated with a cure for HIV, I was able to make insights both into both the value of the basic reproductive ratio, R0, long-term equilibrium viral load values, the size of the target cell population for HIV during both acute and rebound infection, and average life expectancy of an infected cell. These quantities can have potential long term significance in understanding HIV viral dynamics during initial infection, treatment, and rebound, which are crucial if we ever hope to find a cure to this devastating disease.