A mathematical model for HIV treatment with time-varying antiretroviral therapy

Abstract

In treating the human immunodeficiency virus (HIV) infection, strict adherence to drug therapy is crucial for maintaining a low viral load, but the high dosages required for this often have toxic side effects which make perfect adherence to antiretroviral therapy (ART) unsustainable. Even in the presence of drug therapy, ongoing viral replication can lead to the emergence of drug resistance. In this paper, we investigate the effect of immune effectors in modelling HIV pathogenesis during ART, showing a higher rebound for healthy T-cell concentration than drug therapy alone. A periodic model of bang–bang type and a pharmacokinetic model are employed to estimate the drug efficacies. We numerically investigate how time-varying drug efficacy due to drug dosing regimen and/or suboptimal adherence affects the antiviral response and how it affects the emergence of drug resistance. Moreover, we qualitatively characterize successful drugs or drug combination scenarios.

Keywords:

• HIV virus
• differential equations
• helper T-cells
• antiretroviral therapy
• drug resistance
• adherence

2010 AMS Subject Classifications :

• Primary: 92D30
• Secondary: 92B05
• 34A34

Acknowledgements

This research was supported by the US Department of Energy-Northwest Indiana Computational Grid Grant and a CURM mini-grant funded by the NSF grant DMS-0636648.