Modeling HIV-1 dynamics and the effects of decreasing activated infected T-cell count by filtration

Over the past 10 years mathematical models have been developed using differential equations for the progression of HIV-1 to AIDS in an infected patient. Additional terms and formulations are presented over time, as the disease is better understood. Experimentation has been used to obtain many of the modeling parameters. These previous works focus primarily on modeling the progression of the disease, some with intervention such as HAART drugs. Attempts have been made to filter HIV-1 and HIV-1-infected T-cells from the blood. A model is developed that characterizes the rate of filtrations impact on disease progression. Such studies could be also used to investigate the impact of an implantable HIV-1 filter. Proliferation rates of actively and latently infected T-cells are significant and have been incorporated into the models developed in this paper.