Journal of Mathematical Biology

, Volume 48, Issue 5, pp 545–562 | Cite as

Optimal HIV treatment by maximising immune response

  • Rebecca V. CulshawEmail author
  • Shigui Ruan
  • Raymond J. Spiteri


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.


HIV Immune response Optimal control Cytotoxic lymphocytes Numerical methods 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Rebecca V. Culshaw
    • 1
    Email author
  • Shigui Ruan
    • 2
  • Raymond J. Spiteri
    • 3
  1. 1.Department of MathematicsClarke CollegeDubuqueUSA
  2. 2.Department of Mathematics and Statistics / Department of MathematicsSchool of Biomedical Engineering, Dalhousie University / University of MiamiNova Scotia/Coral GablesCanada/USA
  3. 3.Department of Mathematics and Statistics, Faculty of Computer ScienceDalhousie UniversityHalifaxCanada

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