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Resistance to Protease Inhibitors in a Model of HIV-1 Infection with Impulsive Drug Effects

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Abstract

Background

The emergence of drug resistance is one of the most prevalent reasons for treatment failure in HIV therapy. This has severe implications for the cost of treatment, survival and quality of life.

Methods

We use mathematical modelling to describe the interaction between T cells, HIV-1 and protease inhibitors. We use impulsive differential equations to examine the effects of different levels of protease inhibitors in a T cell. We classify three different regimes according to whether the drug efficacy is low, intermediate or high. The model includes two strains: the wild-type strain, which initially dominates in the absence of drugs, and the mutant strain, which is the less efficient competitor, but has more resistance to the drugs.

Results

Drug regimes may take trajectories through one, two or all three regimes, depending on the dosage and the dosing schedule. Stability analysis shows that resistance does not emerge at low drug levels. At intermediate drug levels, drug resistance is guaranteed to emerge. At high drug levels, either the drug-resistant strain will dominate or, in the absence of longer-lived reservoirs of infected cells, a region exists where viral elimination could theoretically occur. We provide estimates of a range of dosages and dosing schedules where the trajectories lie either solely within a region or cross multiple regions.

Conclusion

Under specific circumstances, if the drug level is physiologically tolerable, elimination of free virus is theoretically possible. This forms the basis for theoretical control using combination therapy and for understanding the effects of partial adherence.

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Acknowledgements

R.E.M. is funded by an Ontario Graduate Scholarship. R.J.S. is supported by an NSERC Discovery Grant, an Early Researcher Award and funding from MITACS.

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Authors and Affiliations

  1. Department of Mathematics, The University of Ottawa, 585 King Edward Ave, Ottawa, ON, K1N 6N5, Canada

    Rachelle E. Miron & Robert J. Smith

  2. Faculty of Medicine, The University of Ottawa, 585 King Edward Ave, Ottawa, ON, K1N 6N5, Canada

    Robert J. Smith

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  1. Rachelle E. Miron
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  2. Robert J. Smith
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Correspondence to Robert J. Smith.

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Miron, R.E., Smith, R.J. Resistance to Protease Inhibitors in a Model of HIV-1 Infection with Impulsive Drug Effects. Bull Math Biol 76, 59–97 (2014). https://doi.org/10.1007/s11538-013-9903-9

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