Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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HYBRID ON-OFF CONTROLS FOR AN HIV MODEL BASED ON A LINEAR CONTROL PROBLEM

  • Jang, Tae Soo (Department of Mathematics Inha University) ;
  • Kim, Jungeun (Department of Computational Science and Engineering Yonsei University) ;
  • Kwon, Hee-Dae (Department of Mathematics Inha University) ;
  • Lee, Jeehyun (Department of Mathematics and Department of Computational Science and Engineering Yonsei University)
  • Received : 2014.04.29
  • Published : 2015.05.01
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Abstract

We consider a model of HIV infection with various compartments, including target cells, infected cells, viral loads and immune effector cells, to describe HIV type 1 infection. We show that the proposed model has one uninfected steady state and several infected steady states and investigate their local stability by using a Jacobian matrix method. We obtain equations for adjoint variables and characterize an optimal control by applying Pontryagin's Maximum Principle in a linear control problem. In addition, we apply techniques and ideas from linear optimal control theory in conjunction with a direct search approach to derive on-off HIV therapy strategies. The results of numerical simulations indicate that hybrid on-off therapy protocols can move the model system to a "healthy" steady state in which the immune response is dominant in controlling HIV after the discontinuation of the therapy.

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References

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