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Optimal HIV treatment by maximising immune response

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Abstract.

We present an optimal control model of drug treatment of the human immunodeficiency virus (HIV). Our model is based upon ordinary differential equations that describe the interaction between HIV and the specific immune response as measured by levels of natural killer cells. We establish stability results for the model. We approach the treatment problem by posing it as an optimal control problem in which we maximise the benefit based on levels of healthy CD4+ T cells and immune response cells, less the systemic cost of chemotherapy. We completely characterise the optimal control and compute a numerical solution of the optimality system via analytic continuation.

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Authors and Affiliations

  1. Department of Mathematics, Clarke College, 1550 Clarke Drive, Dubuque, IA 52001, USA

    Rebecca V. Culshaw

  2. Department of Mathematics and Statistics / Department of Mathematics, School of Biomedical Engineering, Dalhousie University / University of Miami, Halifax, Nova Scotia/Coral Gables, B3H 3J5/FL33124-4250, Canada/USA

    Shigui Ruan

  3. Department of Mathematics and Statistics, Faculty of Computer Science, Dalhousie University, Halifax, NS B3H 3J5, Canada

    Raymond J. Spiteri

Authors
  1. Rebecca V. Culshaw
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  2. Shigui Ruan
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  3. Raymond J. Spiteri
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Corresponding author

Correspondence to Rebecca V. Culshaw.

Additional information

Research supported by the Natural Science and Engineering Research Council (NSERC) and the Mathematics of Information Technology and Complex Systems (MITACS) of Canada

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Culshaw, R., Ruan, S. & Spiteri, R. Optimal HIV treatment by maximising immune response. J. Math. Biol. 48, 545–562 (2004). https://doi.org/10.1007/s00285-003-0245-3

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  • DOI: https://doi.org/10.1007/s00285-003-0245-3

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