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A mathematical model for treatment-resistant mutations of HIV
In this paper, we propose and analyze a mathematical model,
in the form of a system of ordinary differential equations, governing
mutated strains of human immunodeficiency virus (HIV) and their
interactions with the immune system and treatments. Our model
incorporates two types of resistant mutations: strains that are not
responsive to protease inhibitors, and strains that are not responsive
to reverse transcriptase inhibitors. It also includes strains that do not
have either of these two types of resistance (wild-type virus) and
strains that have both types. We perform our analysis by changing the
system of ordinary differential equations (ODEs) to a simple
single-variable ODE, then identifying equilibria and determining stability.
We carry out numerical calculations that illustrate the behavior of the
system. We also examine the effects of various treatment regimens on the
development of treatment-resistant mutations of HIV in this model.