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Analysis and dynamic active subspaces for a long term model of HIV
Loudon, Tyson S.
Loudon, Tyson S.
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2015
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Abstract
The Human Immunodeficiency Virus (HIV) disables many components of the body's immune system and, without antiretroviral treatment, leads to the onset of Acquired Immune Deficiency Syndrome (AIDS) and subsequently death. The infection progresses through three stages: initial or acute infection, an asymptomatic or latent period, and finally AIDS. Modeling the entire time course of HIV within the body can be difficult as many models have oversimplified its biological dynamics in the effort to gain mathematical insight but fail to capture the three stages of infection. Only one HIV model has been able to describe the entire time course of the infection, but this model is large and is expensive to simulate. In this paper, we'll show there are two viral free steady states and conduct a stability analysis of one of the steady states. Then, we'll present a reduced order model for the T-cell count 1700 days after initial infection using active subspace methods. Building on the previous results, we'll create a global in time approximation of the T-cell count at any time using dynamic active subspaces.
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