It is recognized that there exist reservoirs of HIV located outside the bloodstream, and that these reservoirs hinder the efficacy of antiretroviral medication regimens in combating the virus. The prevailing theories regarding these reservoirs point to the lymphatic system. In this work, we discuss a novel computational model of viral dynamics in the lymph node, to allow numerical studies of viral “reservoirs” causing reinfection. Our model consists of a system of advection-reaction-diffusion partial differential equations (PDEs), where the diffusion coefficients vary between species (virus, drugs, lymphocytes) and include discontinuous jumps to capture differing properties of internal lymph node structures. We present the mathematical model and discuss our current work on implementing this using the MFEM finite-element infrastructure. Using this model, we analyze the clinical course of HIV infection and the effects of different combinations of anti-retroviral drugs, and then use this model to test the hypothesis whether the lymph node can serve as a reservoir of HIV.
Daniel R. Reynolds
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Yan, Ting, "Advection-Reaction-Diffusion Model of Drug Concentration in a Lymph Node" (2020). Mathematics Theses and Dissertations. 9.