### Mathematical Biosciences and Engineering

2005, Issue 2: 363-380. doi: 10.3934/mbe.2005.2.363

# A mathematical model for treatment-resistant mutations of HIV

• Received: 01 September 2004 Accepted: 29 June 2018 Published: 01 March 2005
• MSC : 37N25.

• 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.

Citation: Helen Moore, Weiqing Gu. A mathematical model for treatment-resistant mutations of HIV[J]. Mathematical Biosciences and Engineering, 2005, 2(2): 363-380. doi: 10.3934/mbe.2005.2.363

### Related Papers:

• 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.

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• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

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